The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  0  1  1  X  0  1  1  X  1  0  0  X  X  1  0  1  X  1  0  X  0  X  X  X  1  X  X  1  0  0  1  X  1  1  0
 0  1  0  0  0  0  0  0  0  1  1  1 X+1  1  X  X  0  1  X X+1  1  0  X  X  1  0  1  X X+1  1  0  1  X  X  1  1  1 X+1  X  1  1  0  1  1  1  0  1  1
 0  0  1  0  0  0  1  1  1  X  1 X+1 X+1  1 X+1  1  1  0  0 X+1  0 X+1  1  1  X  0  0  0  X X+1  1  X  1  1  X  0  X  X  X  1  1  1  X X+1  0  X  0 X+1
 0  0  0  1  0  1  1  0 X+1  X  0  X X+1 X+1  X X+1 X+1 X+1  1 X+1  0  X  X X+1  0  1  X  1  X X+1  X  0  X  0  1  X  0  0  0 X+1  1  X  1  X X+1  0  1  0
 0  0  0  0  1  1  0 X+1 X+1  1  X X+1 X+1  X  1  X  1 X+1 X+1 X+1  0  1  X  1  0  X  X X+1  0 X+1  0  1 X+1 X+1  X X+1  1  1  1  0  0  0  1  0 X+1  0 X+1  0
 0  0  0  0  0  X  0  X  X  X  0  X  X  X  0  X  0  0  X  0  X  0  0  0  0  0  0  X  X  0  0  X  X  0  X  X  0  0  X  0  X  X  0  0  X  X  0  X
 0  0  0  0  0  0  X  0  X  0  X  X  0  0  0  X  X  X  X  X  0  X  X  0  X  X  0  0  X  0  0  X  0  0  X  0  0  0  X  0  X  X  0  X  X  0  0  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+82x^39+131x^40+162x^41+208x^42+240x^43+295x^44+266x^45+289x^46+278x^47+292x^48+296x^49+240x^50+266x^51+235x^52+224x^53+174x^54+128x^55+119x^56+70x^57+48x^58+30x^59+13x^60+6x^61+1x^62+1x^64+1x^68

The gray image is a linear code over GF(2) with n=96, k=12 and d=39.
This code was found by Heurico 1.16 in 1.53 seconds.