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  0  1  1  1  1  1  1 2X  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+2 2X X+1  2  2  1  X 2X+1  1  X  X  0
 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  0  1 2X+2 X+2 X+1 2X  2 2X  X  0  0 X+1
 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  X  0 2X+2 2X  2 X+2  0  1 2X+1 X+2  X X+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  0  X 2X  0  X  X  X 2X  X  0 2X  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+384x^104+390x^105+1308x^107+776x^108+1656x^110+888x^111+2184x^113+1054x^114+2082x^116+1106x^117+2256x^119+962x^120+1650x^122+846x^123+1134x^125+298x^126+354x^128+200x^129+102x^131+30x^132+12x^134+4x^135+2x^138+2x^141+2x^144

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 26.3 seconds.