The generator matrix

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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+618x^107+1524x^108+4914x^109+7044x^110+10416x^111+16608x^112+21966x^113+25050x^114+39048x^115+46638x^116+47962x^117+61440x^118+60168x^119+51600x^120+49878x^121+35622x^122+21318x^123+15942x^124+8046x^125+3058x^126+1632x^127+594x^128+120x^129+42x^130+66x^131+54x^132+36x^133+30x^134+6x^135

The gray image is a linear code over GF(3) with n=531, k=12 and d=321.
This code was found by Heurico 1.16 in 468 seconds.