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 2X  X  1  1 2X  X  X  1  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 X+1  1  1  1  1 2X+1 2X+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  X X+1 X+2  X 2X+1  2  2  2 2X+2
 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  0  0 2X 2X  X  0  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+168x^109+204x^110+88x^111+228x^112+258x^113+68x^114+234x^115+210x^116+6x^117+78x^118+126x^119+30x^120+108x^121+60x^122+18x^123+78x^124+54x^125+2x^126+42x^127+48x^128+26x^129+24x^130+6x^131+2x^132+12x^133+6x^134+2x^141

The gray image is a linear code over GF(3) with n=174, k=7 and d=109.
This code was found by Heurico 1.13 in 0.842 seconds.