The generator matrix

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

generates a code of length 48 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+68x^36+48x^37+94x^38+164x^39+249x^40+260x^41+340x^42+392x^43+431x^44+544x^45+562x^46+628x^47+553x^48+640x^49+658x^50+552x^51+460x^52+424x^53+306x^54+260x^55+195x^56+124x^57+72x^58+48x^59+76x^60+8x^61+14x^62+4x^63+10x^64+2x^66+4x^68+1x^76

The gray image is a linear code over GF(2) with n=96, k=13 and d=36.
This code was found by Heurico 1.16 in 6.25 seconds.