#Java 10, <s>120</s> <s>113</s> <s>112</s> 109 bytes

<!-- language-all: lang-java -->

    n->{var r="|";for(char c,i=0;n++>0;r=n%3<1?c+r:n%3>1?r+c:r,n/=3)c=(char)(i++<1?49:i<3?51:i<4?57:i+61);return r;}

-3 bytes by using part of the trick of [*@Arnauld*'s JavaScript (ES6) answer](https://codegolf.stackexchange.com/a/160550/52210),  
changing `i=0` and `i++<1?49:i<3?51:i<4?57:i+61` to `i=4` and `++i>9?i+55:i>8?57:++i+43`.

Order of output: Highest-to-lowest, `|`-delimiter, lowest-to-highest.

**Explanation:**

[Try it online.](https://tio.run/##hZDBasMwDIbvewpRGNi4TRvS0DWukydYLzuOHTw33dylSlGcwOjy7JnW5joiLPCvD@H/98l2dnE6fA2usk0Dz9bj9QHAYyjpaF0J@z8J8BLI4wc4wQRQah723HyaYIN3sAcEAwMu8mtnCcjMfmb6WJNwnyzd3Ju1RqXylSaDj8kuLpyijG95XJByGc1xaRLpzG1BCqV8vi28StPM509Fusl4otaJ1FSGlhBI94O@W7i07xVbGJ10tT/AmYOIu@nXNyvHEN9NKM9R3YbowiRUKDByYiVvef7l8QTfTPFk6oUtlxw/tR9@AQ)

    n->{                // Method with integer parameter and String return-type
      var r="|";        //  Result-String, starting at the delimiter "|"
      for(char c=64,    //  Character
               i=4;     //  Index, starting at 4
          ;n++>0        //  Loop as long as `n` is larger than 0
                        //  Increasing it by 1 with `n++` at the start of every iteration
          ;             //    After every iteration:
           r=           //     Change the result to:
             n%3<1?     //      If `n` modulo-3 is 0:
              c+r       //       Prepend the character to the result
             :n%3>1?    //      Else-if `n` modulo-3 is 2:
              r+c       //       Append the character to the result
             :          //      Else:
              r,        //       Leave `r` unchanged
           n/=3)        //     Integer-divide `n` by 3
         c=(char)(      //   Set the character `c` to:
             ++i>9?     //    Increase the index `i` by 1 first with `++i`,
                        //    and if it's 10 or larger now:
              i+55      //     Set `c` to the `i-10`'th (0-indexed) letter of the UC alphabet
             :i>8?      //    Else-if `i` is 9:
              57        //     Set `c` to '9'
             :          //    Else (it's lower than 9):
              ++i+43);  //     Set `c` to either '1' or '3' based on the index `i`
       return r;}       //  Return the result-String