The generator matrix

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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+112x^108+684x^110+462x^111+360x^113+216x^114+252x^116+92x^117+2x^126+6x^129

The gray image is a linear code over GF(3) with n=504, k=7 and d=324.
This code was found by Heurico 1.16 in 0.0676 seconds.