The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+69x^44+104x^45+105x^46+170x^47+136x^48+156x^49+159x^50+134x^51+128x^52+120x^53+132x^54+110x^55+110x^56+68x^57+88x^58+74x^59+59x^60+56x^61+27x^62+24x^63+9x^64+8x^65+1x^66

The gray image is a linear code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.16 in 0.414 seconds.