The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+432x^107+278x^108+780x^110+486x^111+780x^113+366x^114+720x^116+318x^117+624x^119+332x^120+426x^122+180x^123+390x^125+144x^126+138x^128+62x^129+72x^131+12x^132+6x^134+6x^135+6x^137+2x^138

The gray image is a linear code over GF(3) with n=174, k=8 and d=107.
This code was found by Heurico 1.16 in 1.01 seconds.