The generator matrix

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

generates a code of length 56 over Z3[X]/(X^2) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+300x^103+402x^104+114x^105+492x^106+576x^107+172x^108+522x^109+588x^110+152x^111+504x^112+414x^113+116x^114+354x^115+348x^116+34x^117+348x^118+264x^119+82x^120+270x^121+222x^122+40x^123+90x^124+84x^125+18x^126+30x^127+12x^128+6x^130+6x^131

The gray image is a linear code over GF(3) with n=168, k=8 and d=103.
This code was found by Heurico 1.16 in 39.4 seconds.