The generator matrix

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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+294x^110+414x^111+288x^112+960x^113+732x^114+216x^115+978x^116+424x^117+324x^118+816x^119+416x^120+144x^121+336x^122+178x^123+12x^125+10x^126+6x^128+10x^129+2x^159

The gray image is a linear code over GF(3) with n=522, k=8 and d=330.
This code was found by Heurico 1.16 in 0.223 seconds.