The generator matrix

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

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+288x^102+1022x^105+1226x^108+1214x^111+902x^114+940x^117+518x^120+284x^123+124x^126+32x^129+6x^132+4x^135

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 0.51 seconds.