Unary, ~6.1*10^4391 bytes
000000000...(more 0s than fits in the observable universe)...000
For reasons that may be somewhat obvious, you can't try this one online.
What the hell is Unary?
Unary is a joke(?) esolang with a pretty basic premise: the only valid symbol is the number 0. To interpret Unary, the 0s are first counted, then that number is converted into binary, then that number is converted into brainfuck (000 corresponds to +, 001 corresponds to -, and so on), then the brainfuck is run.
It's worth noting that you can't distinguish between the numbers 000001 and 001 even though they represent different brainfuck, so in all cases, Unary requires us to include an extra 1 bit at the top of the binary representation: we instead write the binary numbers 1000001 or 1001, which are distinguishable.
Basic overview/comments
Whew, this was a huge pain. As a forewarning, I'm almost certain it's not optimal (there are quite a few structures that are pretty space-inefficient used in the brainfuck) but I'm also almost certain there's no way this is ever fitting on any real computer, so I don't feel too bad about it.
The basic idea for this is probably about what you expect: there's a big array that represents the rest of the code (with a cell set to negative one at the start for navigation), and there's a bunch of code which takes an array and prints out unary code representing the code initializing the array (and the negative one flag), then the code represented by the array.
Obviously it's impossible to test this thing, but I tested the actual quining part on the smallest possible array input ("->+>>" representing "-++"), and it correctly output exactly 19,407,936 0s (corresponding to "->+>>-++"), which is good enough for me.
Finally, I'd like to point out that this is technically a Unary/Lenguage polyglot quine (as all Unary code is also valid lenguage with the same function), though a proper Lenguage golf adapted from this one would probably be a couple hundred orders of magnitude smaller.
Detailed overview
The core idea of this code is to use our array as a base-8 "number", with each entry being another base-8 "digit". We can cascade this downwards (subtract 1 from an entry and add 8 to the one directly after it), and then print a 0 for every entry in the last array entry.
Doing this process on the original array prints Unary code for whatever brainfuck the array represented (the representation is as you might expect: every entry is a different symbol, and every entry contains a number 0-7, one corresponding to each brainfuck command).
You'll note that technically, we're doing this "backwards": printing all the 0s for the code before we print the 0s for the array. I'm not certain that this is necessary, but it does enable us to use some clever constructions later on to save quite a bit of work.
This process, incidentally, will destroy whatever array it's run on. Thus, before we do that, we need to copy the array (actually quite an obnoxious task given that the arrray is variable-length).
Thus after we print the code itself, we have data looking like this:
-1 flag | [original array] | -2 flag | [empty array with the same length] | -3 flag
This means we only need to print the Unary for the array itself, the -1 flag at the start of the array, and the 1 bit at the top of the binary representation which Unary requires.
Fortunately, we can actually use similar code to do this! In order to encode further data, we need to print out 0s in chunks of some very large power of 8: ie, if our code so far was 50 characters long, in order to encode a "-" before the code, we would have to print 8^50 0s.
The power of 8 we have to use is exactly the length of that big empty array. This means that if we put a 1 in the top register of that array, it will increment the last symbol encoded by 1, and if we put an 8 in the top register it will encode a new symbol (specifically a minus).
Furthermore if we move the flag at the end of the array to the right by 1 it'll print out 8 times as many 0s, and thus start editing the symbol before the last symbol encoded!
Since a plus is just "000", we can just move the flag to the right by the value of the last position in the array. This adds as many "000"s to our binary output as there were plusses in the original array representation. When more stuff is added to our array and cascaded down, this will correctly encode the plusses.
We then move the flag at the start of the empty array to the left by 1: this means we start editing the symbol before the plusses we just added. Conveniently, the space it moves into will have been emptied by the operation that moved the end of the array just before now.
All this means that if we put a 2 in the top register of the empty array and then cascade it'll actually print a right carat, and the blank spaces left from moving b will interpret to an appropriate amount of plusses.
We can then repeat this for every single entry in the filled array, thus encoding all of the array representation.
Memory now looks like this
-1 flag|-2 flag| [huge empty array, 2 times as long as the original array]| -3 flag
We now need to add one last minus (to initialize the -1 flag we just got to). All we need to do this is change the minus 2 to a plus 1, then cascade. This both performs the appropriate multiplication by 8, and encodes a -.
Finally, we just need to encode the 1 at the top of the binary representation. To do this, we move b over by 1 one last time and add a 1 at the top, then cascade.
And there it is! We've now printed out 0s representing every part of our original code.
Thank you, and I'm sorry.
Source code
The brainfuck is a little bit long when fully commented (~200 lines), so I'm not certain if I should post it, but I figure y'all can at least have the un-pretty source:
->++>+>+>++>++>+>+>++++++>+>+++>>+++++++>+>++>++++++>>>++++++>+>+>+>++>>>>+++++++>+>+>+>+++>>>++++++>+>+++>>+++++++>+>++>+++++++>>>>++++++>+>+>+>++>>>>+++++++>++>+>+>++++++>+>+++>>+++++++>+>++>+>+>+>+>++>>>++++++>+>+>+++>++>++++++>>>++++++>+>+>+>++>>>>+++++++>+>+>+>+++>>>>>>++++++>+>+>+>+>+++>>>>>+++++++>+>+>+>+>++>+++++++>>>>++++++>+>+>+>++>>>>+++++++>++>>++++++>+>+>+>+>+++>>>>>+++++++>++>+>+>+>+>++>>>+++++++>+>+>+++>>>>>>>>++++++>+>+>+>++>>>>+++++++>+++>+>+>++++++>+>+++>>+++++++>+>++>++>+>+>++++++>+>+>+>++>>>>+++++++>+>+>+>++>++>+>+>++++++>+>+>+++>>>+++++++>+>+>++>++++++>>>>>++++++>+>+>+>+>+>+++>>>>>>+++++++>+>+>+>+>+>+++>>>>>>++++++>+>+>+>+>++>>>>>+++++++>+>+>+>+>+++>>>>++++++>+>+>+++>>>+++++++>+>+>++>+++++++>+>++++++>+>+>+>+>+>+++>>>>>>+++++++>++>+>++++++>+>+>+>+>++>>>>>+++++++>++>>>++++++>+>+>+>+>+>+>+++>>>>>>>+++++++>+>+>+>+>+>+>++>++>>>>++++++>+>+>+>+++>++++++>>>>>++++++>+>+>+>+>+>+++>>>>>>+++++++>+>+>+>+>+>+++>>>>>>++++++>+>+>+>+>++>>>>>+++++++>+>+>+>+>+++>>>>>>>>++++++>+>+>+>+>+>+>+++>>>>>>>+++++++>+>+>+>+>+>+>++>+++++++>>>>>>++++++>+>+>+>+>+>+++>>>>>>+++++++>++>+>++++++>+>+>+>+>++>>>>>+++++++>++>>>++++++>+>+>+>+>+>+>+++>>>>>>>+++++++>++>+>+>+>+>+>+>++>++>>>>+++++++>+>+>+>+++>+++>>>>>>>>>>>>>>++++++>+>+>+>+>+>+>+>+++>>>>>>>>+++++++>>++++++>+>+>+>++>>>>+++++++>+>+>+>+++>++++++>>++++++>+>+>+++>>>+++++++>+>+>+++>>>>>>++++++>+>+>+>+>++>>>>>+++++++>+>+>+>+>+++>>>>>++++++>+>+>+>+++>>>>+++++++>+>+>+>+++>+++++++>++>++>++++++>>++++++>+>+>+++>>>+++++++>+>+>++>>>>>++++++>+>+>+>++>>>>+++++++>+>+>+>++>+++++++>>>++++++>+>+>+++>>>+++++++>+>+>++>++>++>+>+>+>++++++>+>+>+>++>>>>+++++++>+>+>+>++>+>+>+>+>+>++>++>>>>>++++++>+>+>+>+>+++>++++++>>>>>>++++++>+>+>+>+>+>+>+++>>>>>>>+++++++>+>+>+>+>+>+>+++>>>>>>>++++++>+>+>+>+>+>++>>>>>>+++++++>+>+>+>+>+>++>+++++++>>>>>>>++++++>+>+>+>+>+>+>+++>>>>>>>+++++++>++>+>++++++>+>+>+>+>+>++>>>>>>+++++++>++>+>+>+>+>+>++>++>>>>>+++++++>+>+>+>+>+++>+++>>>>>>>>>>>>>>>++++++>+>+>+>+>+>+>+>+>+>+++>>>>>>>>>>+++++++>>++++++>+>+>+>+>++>>>>>+++++++>+>+>+>+>+++>++++++>>>++++++>+>+>+>+++>>>>+++++++>+>+>+>+++>>>>>>++++++>+>+>+>+>++>>>>>+++++++>+>+>+>+>+++>+++++++>>>>++++++>+>+>+>+++>>>>+++++++>+>+>+>++>++>>>>>>>++++++>+>+++>>>>>>>>>++>+++++++>+++>++>+>+>+>+>+>+++>+++>+++>++++++>+>++>++>++++>+++>+++>+++++++>>>>++++++>++++++>+>+>+>++>>>>+++++++>+>+>+>+++>+++>++++++>+>++>++>++>++++>++++>++++>++++>++++>++++>++++>++++>+++>+++>+++>+++++++>>++++++>+>++++++>++>+>++>+++++++>+++>>+++++++>+++>+>++>>>>>>>>>+++>>>>+++++++>+>+>++>+>+>+>+>++++++>+>+>+>+>++>>>>>+++++++>>>>>>++++++>+>+>+>+>+>+++>>>>>>+++++++>>>++++++>+>+>+++>>>+++++++>+>+>+++>>++++++>+>++++++>>>++++++>+>+>+>++>>>>+++++++>+>+>+>++>++++++>+>++>>+++>+++++++>+++>>>>++>+>++++++>+>+>+++>>>+++++++>+>+>+++>+++++++>++>>>+++>+>+>++>>>>>>++++++>++++++>+>+>+>++>>>>+++++++>+>+>+>+++>+++>++++++>+>++>++>++>++++>++++>++++>++++>++++>++++>++++>++++>+++>+++>+++>+++++++>>++++++>+>++++++>++>+>++>+++++++>+++>>+++++++>+++>+>++>>>>>>>>>+++>>>>+++++++>+>+>++>+>+>+>+>+>+>++++++>+>+>+++>>>+++++++>+>+>+++>>+++++++>+>++>>>>>>++++++>>++++++>+>+>+>++>>>>+++++++>+>+>+>+++>+++>++++++>+>++>++>++>++++>++++>++++>++++>++++>++++>++++>++++>+++>+++>+++>+++++++>>>++++++>+>+>++++++>++>+>+>++>+++++++>+++>>>+++++++>+++>+>++>>>>>>>>>+++>>>+++++++>+>++>+>+>+>+>+>++++++>+>+>+>++>>>>+++++++>+>+>+>++>++++++>+>++>>+++>+++++++>+++>>>>++>+>+>++++++>+>+++>>+++++++>+>++>>>>++++++>>++++++>+>+>+>++>>>>+++++++>+>+>+>+++>+++>++++++>+>++>++>++>++++>++++>++++>++++>++++>++++>++++>++++>+++>+++>+++>+++++++>>>++++++>+>+>++++++>++>+>+>++>+++++++>+++>>>+++++++>+++>+>++>>>>>>>>>+++>>>+++++++
>-->>--[-<+]->[++[--->+++]---<++[-<+]->]+++[--->+++]>--[-<+]->---->++[--<>[++[--->+++]---<+++++[----<++++]---->]+++[--->+++]>+[----<++++]>---->++]--<+++++++[--->+++]<--[-<+]->>--[--->+++]--->>--[--<++]-->[++++[-----<+++++]-----<+++++[---->++++]----<+++[--<++]-->]-[-----<+++++]>-[---->++++]>++[------<++++++]------>>+++[---<[++++[-----<+++++]-----<+++++[---->++++]----<+++++++[------<++++++]------>]+++++[-----<+++++]>-[---->++++]>++[------<++++++]>------>>+++]---<<+++++++++++++[-------<+++++++]+[--->+++]---<[+[--<++]--<+++++[---->++++]----<++++[---<+++]---<]>>[+[--<++]-->++++[--->+++]--->]++[--<++]-->>>---[--->+++]--->----->>++++[----<[+++++[------<++++++]------<++++++[----->+++++]----->]++++++[------<++++++]>-[----->+++++]>----->>++++]----<<++++++++++++++[---------<+++++++++]+[---->++++]----<[++[---<+++]---<+++++[---->++++]----<]+++[---<+++]--->>++++++[-<++++++++>]<>-----<<<[->>.<<]+++[[--->+++]---<<[->>>........<<<]+[-[>->]<+]<->++++++++<+++]-->----[---->++++]+++++[-----<+++++]++[--<++]--<+[-[++[--->+++]--->[->+<]<+++>-[--<++]--<]>++<-->+++++[[--->+++]---<<[->>>........<<<]+[-[>->]<+]<->++++++++<+++]-->------[--<++]--<+]->+++++[+[--->+++]---<<[->>>........<<<]++[--[>-->]<++]<->++++++++<++]->-----[--->+++]--->[->+<]<+++>--[-<+]->+++[+[--->+++]---<<[->>>........<<<]++[--[>-->]<++]<->++++++++<++]
The exact number of 0s used is
616143364761046940121393482224894339867345380201767130133313486919095927124457356445367231747521140266173370022946551757495986436536081196868045297628272330390384059772395971191779286883783813697712702083311380720802629542181528279259974270122382291334259076670078283456907144090063837123521728109038972289254725923131778417128787123839239037575809566518515144698909511013229597825122095407702198996899541417882553289474401282217717777845438435506256387112472797473268235689408744655098869728879606757978358505806156421963379547318142883884528468751816610374042589741195416986282360597637951748580316227437951083206547340002950237138353873683827224872420688269051148041914106540181545636126975204020515616888610209347943212212684032994981872040279134760921950441974664462626740824769006477972532358261625821022468550562561067773665916456352101740599621566669636512759138416019741339956533219082231457782020998061560188458949523569043543472825311694153186492127832152368263433627346401816742081184272285138868588737702544161051266511345401776302508848404989044851701234612868569930533447734786659774504348270829815069786996595352931052563253833910670459061338664835111006064026972821593395459376847379338727645638102959876509529598180508190944759740278032543135323831096032264282759700516599819159593380726609694016158768372040897232130064627016970719454234890810133557942103242082428193652525717784679766009840567745646644331050845934041815088097332504352438215802005681361724732417128846494405432135929762912067831306775322080038483165731774473085357566563624402414177907348890170209026776293825006497117681077216606902562225184543780956129658804093641090955334441702108200564658744439989789201224157261892503165643308457788492416371138829568712401818445624554600923862455172225972137155277042400428634635794267865563766239731245919228046855426376607293646700303578427596008362291239931429658436763436719678326692915408656227680419507941034924280704994802195387552837470839012206296262948274121554534825929221937317579576287409893717258523001476821273741591905466514991100795003027995820718624627560000685829593037893516218245771605918736777569490302646860116831211143429524438818972119953427472167111184521816913965170021208796837058611193110390517567196364486837447552746813630060986477162908564149642028449379763465797559696051374230746360712939114777230926431439196151657705180265020483638629061181115856223950249806419818375856529987900246040227082601855626646444080216637310658434683889414278770982063250184353729183793452944251724697854181617951614799763586644028479802980036647045105801552589931160634006431597294780772117688186110086846079813170103829768160563126247208942693587842950980471492950218296552846456932278774596999132699204842933464261728949352373762279520360130690593476460298502885309846199176184758132580237138986886575217114963071503275472309839043003811612480724199448586309349213643468070828586583244591263370384564485550086863984151080517206405235910197380819828141069270492593578986828345436437174028486982241355518138451897126139232242703752607826960024771549490116659322453183855123857138475614101348080310760135256588738232612996648332732281155595814319181966181574401320500067489163573212418944844484950259082074896272135947770797061836016279282123019467117684670513267319113631747092736545960755034809236690912731932588771491682676453979945982754468716932978590114642741630083944274379070387978397185461190324579966999262505612480431374579002240579057976399577489156724969889391725011201833796208889208642431523656036515892951544697280547449403879151875515288785339517008449261777065296448378328263083714549226346273500515673503831635754141766922846713000935292132391822069931132294405910519960461798776924488932623464859144582786720457864275598371518594949910770504649195142874620028228890448589489597208338562687621880437805894822197524541279873734273522403771848708628352939445662430217734644866430785751657273790572085485900108956813143322699032604055731135389248624818347278303261582515845621280853277496120155330289546717304073439125810011869192307295393119864362022104242206053603655047887527558361040028989920694801323274066616457054148538214643602629113440692125709885109559566032777838457552957583786148605526507117591555800832794105245862353696525934364943795116979478987279494334241959368528163214344004159915398916504737171079910682142420502023