The generator matrix

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

generates a code of length 31 over Z3[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+258x^56+202x^57+354x^59+160x^60+300x^62+148x^63+282x^65+122x^66+204x^68+74x^69+60x^71+20x^72+2x^81

The gray image is a linear code over GF(3) with n=93, k=7 and d=56.
This code was found by Heurico 1.16 in 0.0926 seconds.