The generator matrix

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

generates a code of length 32 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+106x^54+94x^57+124x^60+486x^62+96x^63+972x^65+66x^66+70x^69+78x^72+50x^75+22x^78+16x^81+4x^84+2x^93

The gray image is a linear code over GF(3) with n=96, k=7 and d=54.
This code was found by Heurico 1.16 in 0.841 seconds.