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  1  X  1  X  1  1  1  1  1  X  1  1  1  1  1  X  X  1  1  1  X
 0  X  0  0  0  0  0  0  0  0  X  X  0  0  0  X  0  0  0  0  X  X  X  X  0  X  X  0  X  X  X  X  X  X  0  X  X  0  X  X  X  X  X  X  0  0  0  X  X  0  X  X
 0  0  X  0  0  0  0  0  0  X  X  X  0  X  X  0  0  0  X  X  X  X  X  X  0  X  0  X  0  0  0  X  0  X  X  0  X  0  X  X  0  0  X  0  X  0  0  0  0  0  X  X
 0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  X  0  X  X  0  0  0  0  0  X  0  X  0  X  X  X  X  X  X  0  0  X  X  0  0  0  0  0  0  X  X  0  0  X  X  0  0
 0  0  0  0  X  0  0  0  X  0  0  X  X  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  X  0  X  0  0  X  X  0  0  0  0  X  0  X  X  X  0  0  0  0  0  X  X  0
 0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  X  0  X  X  0  0  0  0  X  X  0  0  X  0  0  0  X  X  X  0  X  X  X  X  0  0  0  X  X  0  0  X  0  0  X  X  X
 0  0  0  0  0  0  X  0  X  X  X  0  0  0  X  X  X  0  0  X  0  0  X  0  X  0  X  0  0  X  X  0  X  0  0  0  0  X  0  X  X  X  X  0  X  X  X  0  0  0  X  X
 0  0  0  0  0  0  0  X  X  X  0  0  X  X  X  0  X  0  X  0  0  X  X  0  0  0  X  X  0  X  0  0  0  X  X  0  X  X  0  0  0  X  0  0  0  X  0  X  0  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+38x^44+4x^46+96x^48+60x^50+142x^52+60x^54+60x^56+4x^58+25x^60+19x^64+2x^68+1x^92

The gray image is a linear code over GF(2) with n=104, k=9 and d=44.
This code was found by Heurico 1.16 in 0.0685 seconds.