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  X  X  1  X  1  1  1  1  X  1  1  X  1  1  X  1  1  X  1  X  1  X  X  X
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  0  X  X  X  X  0  X  X  0  X  0  X  X  X  X  0  X  0  X  X  0  0  X  0  X  X  X  0  0  X  0  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  X  X  X  0  X  0  X  0  0  0  X  0  X  X  X
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  X  X  X  0  X  0  X  0  X  0  0  0  X  0  X  0  0  0  X  0  X  X  X  X  0  0  X  0  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  X  0  0  X  0  X  X  0  0  0  0  X  0  0  0  0  X  X
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  0  0  X  0  X  X  X  X  0  X  X  0  X  0  0  X  X  X  X  X  X  X  0  X  0  0  X  0  X  X  0  X
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  X  X  0  0  X  0  0  0  X  0  X  X  X  X  0  0  X  X  X  0  0  X  0  0  0  X  X  X  X  X  X
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  0  X  X  X  X  X  0  X  X  0  X  X  0  X  X  X  0  0  0  X  X  0  X  0  0  0  X  0  X  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  0  0  X  0  X  0  0  X  0  X  0  X  0  0  X  0  0  X  X  0  0  X  X  X  X  X  0  X  X  0  X

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+84x^44+14x^46+172x^48+84x^50+198x^52+112x^54+163x^56+44x^58+90x^60+2x^62+45x^64+11x^68+3x^72+1x^84

The gray image is a linear code over GF(2) with n=106, k=10 and d=44.
This code was found by Heurico 1.16 in 0.227 seconds.