The generator matrix

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

generates a code of length 59 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+136x^108+402x^109+298x^111+756x^112+434x^114+852x^115+394x^117+726x^118+294x^120+612x^121+258x^123+414x^124+208x^126+390x^127+88x^129+162x^130+62x^132+48x^133+4x^135+12x^136+2x^138+2x^141+4x^144+2x^147

The gray image is a linear code over GF(3) with n=177, k=8 and d=108.
This code was found by Heurico 1.16 in 0.637 seconds.