The generator matrix

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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+138x^109+342x^110+64x^111+366x^112+522x^113+400x^114+570x^115+1782x^116+690x^117+666x^118+540x^119+24x^120+78x^121+78x^122+12x^123+60x^124+54x^125+2x^126+42x^127+72x^128+20x^129+24x^130+12x^131+2x^159

The gray image is a linear code over GF(3) with n=522, k=8 and d=327.
This code was found by Heurico 1.16 in 0.607 seconds.