The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X X 1 1 1 1 1
0 X 0 0 0 0 0 0 0 0 X X X X X 2X 2X 2X 0 2X 2X X X X 0 X X X 0 2X 0 0
0 0 X 0 0 0 0 0 X X 2X 2X 2X X 2X 0 2X 2X X 0 2X 0 X X 0 2X 2X 0 X 2X 0 0
0 0 0 X 0 0 0 X 2X 2X 2X X X 0 0 X 0 0 X 0 2X X 0 2X X X 0 X 0 2X X 0
0 0 0 0 X 0 0 2X 2X X X 0 2X 2X 2X X 0 0 0 X 2X X 2X X 0 X X 0 X X X 0
0 0 0 0 0 X 0 2X X 2X X 2X 0 2X 2X 0 0 X X 2X X X X 0 2X 0 X 0 X 2X X 0
0 0 0 0 0 0 X X 0 X 0 X 0 2X 0 2X 2X 0 2X X 0 X X X X X 2X 2X 0 X X 0
generates a code of length 32 over Z3[X]/(X^2) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+38x^48+152x^51+202x^54+54x^56+226x^57+432x^59+230x^60+1296x^62+298x^63+1728x^65+268x^66+864x^68+238x^69+238x^72+164x^75+80x^78+44x^81+6x^84+2x^87
The gray image is a linear code over GF(3) with n=96, k=8 and d=48.
This code was found by Heurico 1.16 in 0.456 seconds.