The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  0  1  1  1  0  X  1  1  1  1  1  1  0  1  1  1  0  0  1 2X  1  1  1  1  1  1  1  1  1  1  1  1 2X  X  0  1  0  1  X  1  X  1  1  1  1
 0  1  1  2  0  1  2  1  0 2X+1  2  1  0  2 2X+1  1  1 X+2  0 2X+1  0 2X+1  2  1  0  2 2X+1  1  1  X  1  X  2 2X+1 X+1  0 2X 2X+2  X  2 X+1 X+1 X+1  1  1  X X+2  X  0 2X 2X  0  2 X+1  0  0
 0  0 2X  0  0  0  0  0  0 2X  X 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0  X  0 2X  0  X  0 2X  0  X  0  0 2X  X 2X  X  X  X  X  X 2X  X 2X  0 2X 2X  X 2X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0 2X  X 2X  X  0  X  X 2X 2X  X  0  X  X  0  X  0  0  X 2X  X 2X 2X  X 2X  X  X  X  X  X  0 2X  0  0  0  0 2X  X 2X 2X 2X  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0 2X 2X  X  0 2X  X 2X  0 2X  X 2X  0 2X 2X  0 2X  X 2X 2X  X  0  X  X  0  X 2X  0 2X 2X  X  X 2X  0  X  X 2X  X 2X 2X  X 2X  X
 0  0  0  0  0 2X  0  0  X 2X 2X  X 2X  0 2X 2X 2X  X  0  0  0  X  X  X  0  0  0  X 2X  X 2X 2X  0  0 2X  0  0 2X 2X 2X  X  0  0  0  X 2X  0  X  0  X 2X  0  0  X  0  X
 0  0  0  0  0  0  X  0  X  0  X  X  X 2X 2X  0  X 2X 2X  0 2X  X 2X  0  0 2X  X 2X  0 2X  0  X 2X 2X  X 2X  X  X 2X 2X 2X  X 2X  X  0  X 2X 2X  X 2X  X 2X  0  X  X  0
 0  0  0  0  0  0  0  X  X  X  X  0 2X  X 2X  X  X  X  X 2X 2X 2X  X  0  X  X 2X  X  X  0  X  0  0 2X  X 2X 2X  X  X  0  0  X 2X  X  0  X 2X  0 2X  X  0  0 2X 2X  0  0

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+66x^90+274x^93+24x^94+36x^95+556x^96+84x^97+186x^98+1050x^99+312x^100+528x^101+1794x^102+738x^103+930x^104+3222x^105+1488x^106+1602x^107+4352x^108+2418x^109+2652x^110+5674x^111+2700x^112+2802x^113+5682x^114+2586x^115+2250x^116+4624x^117+1770x^118+1338x^119+2862x^120+750x^121+606x^122+1470x^123+216x^124+174x^125+646x^126+36x^127+18x^128+280x^129+130x^132+88x^135+24x^138+10x^141

The gray image is a linear code over GF(3) with n=168, k=10 and d=90.
This code was found by Heurico 1.16 in 45.7 seconds.