The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+142x^102+84x^103+168x^104+612x^105+270x^106+306x^107+1222x^108+510x^109+510x^110+1426x^111+582x^112+690x^113+1782x^114+816x^115+822x^116+1760x^117+840x^118+972x^119+1654x^120+696x^121+486x^122+1324x^123+372x^124+330x^125+686x^126+162x^127+84x^128+224x^129+42x^130+6x^131+58x^132+24x^135+8x^138+4x^141+6x^144+2x^147

The gray image is a linear code over GF(3) with n=174, k=9 and d=102.
This code was found by Heurico 1.16 in 5.26 seconds.