The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  1  1  0  0  1  0  X  1  X  X  1  1  1  1  0  1  1  X  1  X  1  0  0  1  X  X  0  0  0  X  0  1  0  1  1  X
 0  1  0  0  1  1  1  0  X  1 X+1  1  1  0  1 X+1  X  X  0  1  X  1  0  1  1  1  X X+1  0  X  1  1 X+1  X X+1  1  0  1  1  1  1  X  0  1  1  1  X  1  X  1  X  X
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  1  1  X  X  0  1  0 X+1 X+1  1  X X+1  0  1  1  0  X  0 X+1 X+1  1  0  X  X  1 X+1  0  0  1  1  X  0  X  1 X+1  1  X  0  X
 0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  X  X  X  0  0  0  X  0  X  X  X  X  X  X  X  X  0  X  0  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  0  X  0  0  0  X  X  0  0  0  X  X  0  X  X  0  0  X  X  X  0  X  0  0  X  0  0  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  X  0  X  X  X  0  0  0  0  X  X  0  X  X  X  0  X  X  X  X  X  X  X  X  X  X  X  0  X  0  X  X  X  0  X  0  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  X  X  0  X  0  0  X  X  0  X  0  X  X  X  0  X  X  0  X  X  X  0  X  X  0  0  0  X  0  X
 0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  X  X  X  0  0  X  0  X  X  0  0  0  X  X  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  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+127x^44+216x^46+329x^48+250x^50+335x^52+216x^54+207x^56+164x^58+109x^60+48x^62+38x^64+2x^66+5x^68+1x^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 0.487 seconds.