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  1  1  1  1  1  1  1  1  1  X  X  X  X  1  1  X  X  X  1  1  1  1  1  1  1  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  X  X  0  0  X  X  X  X  X  X  X  X  0  0  0  X  X  X  X  0  0  X  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  0  0  X  X  X  0  0  X  X  0  X  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  X  X  X  0  X  0  0  X  X  0  0  0  X  X  X  0  X  X  0  X  0  X  X  0  0  0  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  0  X  0  0  X  X  X  0  X  X  X  0  X  X  0  X  0  0  X  X  0  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  0  X  X  0  0  0  X  X  0  X  0  X  0  X  0  X  X  X  X  X  0  X  0  X  X  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  0  X  0  X  0  X  0  X  X  X  X  X  X  X  0  0  X  X  X  0  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  0  0  X  X  X  0  0  X  X  0  X  X  0  X  X  X  X  0  X  0  X  X  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  X  X  X  X  0  0  0  X  0  X  X  X  0  X  X  X  X  X  X  X  X  X  X  0  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  X  0  X  X  0  0  X  0  X  X  X  0  0  X  X  X  0  0  0  0  X  X  X  X  X  0  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+83x^40+187x^44+16x^46+297x^48+240x^50+413x^52+240x^54+314x^56+16x^58+141x^60+70x^64+27x^68+2x^72+1x^88

The gray image is a linear code over GF(2) with n=104, k=11 and d=40.
This code was found by Heurico 1.16 in 0.693 seconds.