The generator matrix

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

generates a code of length 32 over Z3[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+204x^55+290x^57+558x^58+440x^60+876x^61+454x^63+1032x^64+492x^66+978x^67+326x^69+564x^70+130x^72+150x^73+42x^75+12x^76+8x^78+4x^84

The gray image is a linear code over GF(3) with n=96, k=8 and d=55.
This code was found by Heurico 1.16 in 20.4 seconds.