The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+66x^41+95x^42+154x^43+304x^44+284x^45+379x^46+432x^47+446x^48+506x^49+520x^50+620x^51+584x^52+608x^53+593x^54+496x^55+466x^56+430x^57+344x^58+290x^59+212x^60+132x^61+97x^62+48x^63+29x^64+22x^65+16x^66+8x^67+4x^68+3x^70+2x^72+1x^74

The gray image is a linear code over GF(2) with n=104, k=13 and d=41.
This code was found by Heurico 1.16 in 7.34 seconds.