The generator matrix

 1  0  0  0  1  1  1  1 2X  1  1  1  1  0  X  1  X  1  1  1  1  0  1  X  1  1  1  1  1  1  X  0
 0  1  0  0  0  1 2X  2  1 2X+1 X+2 2X X+2  1  X 2X+2  1 X+2  0 X+2  1  1 X+1  1  0 X+2  X X+1  0  2  1  1
 0  0  1  0  0  2 2X+1  2 2X  X X+1 2X+2 2X+1 X+1  1  2  1  1 2X+2 2X+2 X+1 2X  0 X+2 2X 2X 2X+1 2X X+2 2X+1  2 X+1
 0  0  0  1  1 X+1 2X+2 2X 2X+1  2 2X 2X+2 X+1  X  2 X+1 X+1 2X+2  X  2 2X+1  2  1 X+1  1  2 2X+2 X+2 2X+1 2X 2X+1  1
 0  0  0  0 2X 2X  X  0 2X 2X 2X 2X  0 2X 2X  X  X  0 2X  X  X  0  0  0  X 2X  0  0  0  X 2X  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+596x^54+1982x^57+3474x^60+4002x^63+4944x^66+3378x^69+1146x^72+144x^75+6x^78+6x^81+4x^84

The gray image is a linear code over GF(3) with n=96, k=9 and d=54.
This code was found by Heurico 1.16 in 2.36 seconds.