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

generates a code of length 59 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+274x^108+360x^114+600x^117+540x^120+180x^123+136x^126+80x^135+12x^144+2x^153+2x^162

The gray image is a linear code over GF(3) with n=177, k=7 and d=108.
This code was found by Heurico 1.16 in 2.39 seconds.