Print a Ternary Value Put simply, you are to print out the following number:
0202020100110020122120012121100120121020202100012110002002010110211221012021112010200012112021220120022222102211121110110201220020202001111212210010100222100112101201122100222120201002002020200011110002211002202100022210212020112002020000120222111121112002112101000011112021202002210220022121002011021000202102101010210220022011011210102021110111212122201122021101211110121100111110122110110201011100022000212022020110211221022001201211120110221212221012220101121222011202112012221010212021120022110020022202020212022222012000012111001022021211110221211001201020202020011122222010010112222002010220111111111101010220120110010102100211000120111022212000220210121222000020212112010102012210201021022020202102102002011100211022101011202222111120100000021221101221220220200102010010021110120012202111012000100021102111102220102021100021001010020020001001222220121221122100102020000000221101220111201210200212111010211122211011210012020010012110110021221010121121202220001112220120221112001021001211112211110112212100001212200021111011200010120221010201110201121021002201221111210102010200200210112020022102110212020112111000121001021202101012000112210101112122220120012022121202101110221120012122120220120010122102110102002222120201102002111100001021001121100211122200011102122022110122000102212201111020200010222211002210021200202210102022221022222101121020102100100111221102211100102000211010012201121121220122021122102201000011221122101101111201102120001002012211020211122102002211111121222112110222212012201221111222010100101120022022111002012122112201212201011022212100010001022010102100120112001012110202210101220021102112210122210010202011211010002122111111221121222002211200201122010022021011110112111020102102001110000201111222220120011111112102212011200021210100210100010

This is a randomly generated string of zeroes, ones, and twos. It is 1777 characters long. You may be asking: what makes this challenge interesting or unique?
In normal text compression you would be able to get this down to roughly 29% of its initial size. However, if you were to use a base-4 compression - i.e. using two bits per character - you could actually get that down to 25% of its initial size. The point here is that simply compressing this file will likely not be enough to win this challenge. And, base-4 or base-8 (etc...) compression may not actually be the best solution, because no powers of 2 can be evenly divided by 3. So, you will need to get creative!
Other
-You are allowed to have a trailing newline after the output
-This challenge was inspired by this question and, while it is true that the premises are largely the same, the biggest and most important difference between the two are that this challenge in not in a friendly base (the linked question is effectively in base-4, which makes compression relatively nice).
-Other than the optional trailing newline, you must output the string/number exactly (i.e. no switching those characters for different characters), as this is kolmogorov-complexity
Scoring
This is code-golf. Shortest code in bytes wins! [If you wish, you can also try to solve this in as few characters as possible - but make sure you still include the byte count]
JavaScript (Node.js),  504 481  474 bytes
Builds a BigInt from a string encoded in base 126 and converts it to base 3.
Because the data string contains many unprintable characters, it is not shown at all below.

_=&gt;0+Buffer(`...`).reduce((n,v)=&gt;n*126n+BigInt(v-1),0n).toString(3)

Try it online!
The theoretical length of the string is:
$$\left\lceil\frac{\log(3^{1777})}{\log(126)}\right\rceil=404$$
Because a few characters need to be escaped, we actually need \$410\$ bytes to store it in the source.