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

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+330x^108+324x^114+36x^117+36x^126+2x^162

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 92.5 seconds.