The generator matrix

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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+134x^102+132x^103+150x^104+672x^105+276x^106+324x^107+600x^108+300x^109+294x^110+644x^111+150x^112+234x^113+568x^114+210x^115+198x^116+464x^117+210x^118+144x^119+294x^120+114x^121+66x^122+146x^123+54x^124+18x^125+96x^126+12x^127+30x^128+26x^129

The gray image is a linear code over GF(3) with n=168, k=8 and d=102.
This code was found by Heurico 1.16 in 0.516 seconds.