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  0  1  1  0  1  1  0  0  1  1  0  X  1  0  1  X  1  1  1  1  X  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  1  1  X X+1  1  0  1  1  1 X+1 X+1  1  1 X+1  1  0  1  1  0  X X+1  1  0 X+1  X  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  0  X  X  X  X  X  X  X  0  X  0  X  0  X  X  0  0  X  X  X  X  X  X  X  X  X
 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  X  X  X  0  X  0  X  X  0  0  X  X  X  X  X  0  0  X  0  0  X  0  X  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  X  0  X  0  0  X  X  0  0  0  0  X  0  X  0  X  0  X  X  X  X  0  0  X  X  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  X  0  0  0  0  X  X  X  0  0  0  0  X  X  0  0  X  0  0  0  X  X  X  X  0  0  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  0  X  X  0  0  0  0  0  0  X  0  X  0  0  0  0  X  X  0  X  0  0  X  X  0  0
 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  X  X  X  0  X  0  0  0  0  X  X  X  0  X  X  0  X  X  X  X  X  X  0  X  0  X  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  X  0  X  0  X  0  0  X  0  0  X  X  X  X  0  X  0  0  0  X  X  X  X  X  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+113x^44+100x^46+301x^48+232x^50+323x^52+224x^54+327x^56+184x^58+151x^60+28x^62+34x^64+21x^68+9x^72

The gray image is a linear code over GF(2) with n=106, k=11 and d=44.
This code was found by Heurico 1.16 in 0.557 seconds.