The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+456x^104+416x^105+1272x^107+674x^108+1740x^110+890x^111+1974x^113+1094x^114+2124x^116+1188x^117+2112x^119+988x^120+1944x^122+766x^123+990x^125+366x^126+432x^128+118x^129+72x^131+44x^132+6x^134+12x^135+2x^138+2x^141

The gray image is a linear code over GF(3) with n=174, k=9 and d=104.
This code was found by Heurico 1.16 in 8.75 seconds.