The generator matrix

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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+194x^108+324x^111+90x^114+48x^117+36x^120+18x^123+18x^129

The gray image is a linear code over GF(3) with n=168, k=6 and d=108.
This code was found by Heurico 1.16 in 0.022 seconds.