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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+194x^108+438x^111+950x^114+2916x^116+1544x^117+186x^120+92x^123+136x^126+96x^129+2x^132+4x^135+2x^171

The gray image is a linear code over GF(3) with n=522, k=8 and d=324.
This code was found by Heurico 1.16 in 0.301 seconds.