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

generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+190x^108+60x^111+180x^114+210x^117+66x^120+10x^126+10x^135+2x^153

The gray image is a linear code over GF(3) with n=171, k=6 and d=108.
This code was found by Heurico 1.16 in 0.0962 seconds.