The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+138x^109+246x^110+66x^111+318x^112+246x^113+58x^114+120x^115+150x^116+36x^117+162x^118+120x^119+54x^120+84x^121+84x^122+14x^123+66x^124+78x^125+6x^126+42x^127+30x^128+4x^129+30x^130+12x^131+12x^133+6x^134+2x^138+2x^144

The gray image is a linear code over GF(3) with n=174, k=7 and d=109.
This code was found by Heurico 1.16 in 0.197 seconds.