The generator matrix

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

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+162x^52+570x^53+568x^54+1128x^55+1458x^56+1466x^57+2520x^58+2892x^59+2484x^60+3936x^61+4584x^62+3378x^63+5574x^64+5568x^65+3762x^66+4956x^67+4290x^68+2634x^69+2796x^70+2118x^71+882x^72+732x^73+354x^74+116x^75+66x^76+36x^77+12x^78+4x^81+2x^93

The gray image is a linear code over GF(3) with n=96, k=10 and d=52.
This code was found by Heurico 1.16 in 19.6 seconds.