The generator matrix

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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+156x^106+354x^107+884x^108+558x^109+594x^110+678x^111+444x^112+336x^113+984x^114+402x^115+306x^116+438x^117+198x^118+180x^119+6x^120+24x^121+6x^122+4x^123+6x^125+2x^150

The gray image is a linear code over GF(3) with n=504, k=8 and d=318.
This code was found by Heurico 1.16 in 0.155 seconds.