The generator matrix

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

generates a code of length 48 over Z2[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+72x^39+146x^40+152x^41+223x^42+246x^43+273x^44+284x^45+244x^46+282x^47+296x^48+310x^49+292x^50+264x^51+211x^52+202x^53+182x^54+132x^55+117x^56+66x^57+48x^58+26x^59+12x^60+10x^61+2x^62+2x^63+1x^74

The gray image is a linear code over GF(2) with n=96, k=12 and d=39.
This code was found by Heurico 1.10 in 0.547 seconds.