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.