The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+129x^40+466x^42+930x^44+1351x^46+1800x^48+2199x^50+2468x^52+2314x^54+1985x^56+1440x^58+714x^60+379x^62+147x^64+39x^66+16x^68+4x^70+1x^72+1x^88

The gray image is a linear code over GF(2) with n=104, k=14 and d=40.
This code was found by Heurico 1.16 in 50.5 seconds.