The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+234x^101+274x^102+600x^103+822x^104+890x^105+1524x^106+1776x^107+1330x^108+2232x^109+2676x^110+1934x^111+3174x^112+3150x^113+2620x^114+3918x^115+3702x^116+2820x^117+3888x^118+4098x^119+2332x^120+3198x^121+2994x^122+1848x^123+2058x^124+1626x^125+840x^126+990x^127+642x^128+336x^129+246x^130+144x^131+58x^132+42x^133+6x^134+22x^135+2x^138+2x^141

The gray image is a linear code over GF(3) with n=174, k=10 and d=101.
This code was found by Heurico 1.16 in 50.3 seconds.