The generator matrix

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

generates a code of length 32 over Z3[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+54x^52+84x^53+320x^54+432x^55+294x^56+498x^57+1008x^58+600x^59+1074x^60+1608x^61+846x^62+1654x^63+2184x^64+1236x^65+1532x^66+2058x^67+912x^68+948x^69+1146x^70+312x^71+412x^72+246x^73+90x^74+68x^75+12x^76+30x^78+16x^81+8x^84

The gray image is a linear code over GF(3) with n=96, k=9 and d=52.
This code was found by Heurico 1.16 in 57.9 seconds.