The generator matrix

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

generates a code of length 32 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+86x^45+12x^47+166x^48+60x^50+392x^51+672x^53+762x^54+2328x^56+1486x^57+5172x^59+2856x^60+8808x^62+4566x^63+10644x^65+4536x^66+7728x^68+2826x^69+3480x^71+1198x^72+462x^74+422x^75+232x^78+110x^81+32x^84+12x^87

The gray image is a linear code over GF(3) with n=96, k=10 and d=45.
This code was found by Heurico 1.16 in 18.3 seconds.