The generator matrix

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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+240x^107+866x^108+522x^109+774x^110+980x^111+462x^112+402x^113+754x^114+438x^115+480x^116+526x^117+24x^118+36x^119+14x^120+12x^121+6x^125+2x^126+6x^128+14x^129+2x^132

The gray image is a linear code over GF(3) with n=504, k=8 and d=321.
This code was found by Heurico 1.16 in 0.149 seconds.