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  1  1  1  X  1  0  1  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 2X+1  1 2X+1  1 2X+1  1  0 2X+1
 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+1 2X+1  0 2X+1  X 2X 2X+1 X+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  2  1  1  X  X  X  X 2X+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+318x^56+286x^57+858x^59+378x^60+864x^62+520x^63+954x^65+466x^66+798x^68+396x^69+468x^71+118x^72+114x^74+22x^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 0.485 seconds.