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

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+76x^108+378x^112+144x^114+648x^115+648x^118+270x^121+4x^135+18x^141

The gray image is a linear code over GF(3) with n=522, k=7 and d=324.
This code was found by Heurico 1.16 in 0.0947 seconds.