The generator matrix

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

generates a code of length 32 over Z3[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+336x^56+282x^57+762x^59+456x^60+954x^62+412x^63+924x^65+522x^66+876x^68+318x^69+414x^71+172x^72+108x^74+24x^75

The gray image is a linear code over GF(3) with n=96, k=8 and d=56.
This code was found by Heurico 1.16 in 0.543 seconds.