The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+156x^106+300x^107+122x^108+462x^109+480x^110+140x^111+504x^112+546x^113+126x^114+522x^115+468x^116+80x^117+348x^118+408x^119+118x^120+468x^121+306x^122+78x^123+276x^124+276x^125+18x^126+144x^127+102x^128+22x^129+36x^130+30x^131+10x^132+4x^135+6x^138+2x^141+2x^147

The gray image is a linear code over GF(3) with n=174, k=8 and d=106.
This code was found by Heurico 1.16 in 0.553 seconds.