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  1  1  1  1  X  1
 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  0  X  X  0  0
 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  X  0  X  X  0
 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  X  0  X  0  X  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  X  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  0  0  X  X  X  0
 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  X  X  0
 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  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+31x^44+39x^46+40x^48+94x^50+120x^52+96x^54+30x^56+14x^58+25x^60+9x^62+8x^64+4x^66+1x^96

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 0.062 seconds.