Japt, 50 49 bytes
`mcnhp4 bn26 3hsvn2Ô©u6pn8t4n4v l2`qÍ®nH3ÃùT20 Õ·
My idea was to compress the 10 columns as base-3, left-pad each with zeroes to length 20, and transpose. I think this is more optimal than compressing the 11 rows as base-3 and prepending 9 rows of zeroes, which seems to be the strategy most submissions are using right now.
The idea used by Nick Kennedy's clever Jelly solution doesn't translate to Japt because it doesn't have support for bigints without hooking into JS, and when you leave Japt-land you don't get compression, so the program ends up quite a bit longer.
Japt -R
, 4647 bytes
`mcnhp4bn263hsvn2Ô©u6pn8t4n4vl2`qÍ®nH3ÃùT20`l2n4v8t4nu6pn2Ô©3hsvn26ebnhp4nmc`qÍ®nH3ÃùT20
Output rotated 90 degrees.