The generator matrix

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

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+167x^44+160x^46+315x^48+224x^50+374x^52+224x^54+258x^56+160x^58+115x^60+30x^64+16x^68+4x^72

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 8.77 seconds.