The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  1  0  X  0  1  0  1  X  1  X  1  1  1  0  1  1  1  X  X  X  1  1  1  X  1  0  0  1  0  1  1  1  1  1  0  X  0  1  X  1  1  1
 0  1  0  1  0  1  1  0  0  1 X+1  X  1  1  0  X  0 X+1  1 X+1  1  1  0  1  X  X  0  0  1  1  1  1  1  1  0  1  0  X  X  1  X  X  X  1  0  1  1  1  X  1  0 X+1  0
 0  0  1  1  1  0  1  0  1 X+1  X  1  X  1  1  0  1 X+1  X  X  1  1  0  1  1  0  X  1  0  1 X+1  0  1  1  1 X+1  1  1  0  X  1  0  X  0  1  1  0 X+1 X+1  X  1  X  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  0  X  0  X  0  0  0  0  0  X  X  0  X  X  0  X  X  X  X  X  0  X  X  X  X  0  0  X  0  0  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  0  X  0  0  X  0  0  X  X  0  X  X  X  X  0  0  X  0  0  0  X  X  X  0  0  0  0  X  0  0  X  X  0  0  0  X  X
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  X  0  X  0  X  X  0  0  0  0  0  0  0  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  X  X  0  X  0  X  0  X  X  X  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  X  X  0  0  X
 0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  X  0  X  0  X  0  0  X  X  X  0  X  0  0  0  0  X  0  0  X  0  0  X  0  X  0  X  X  X  X  0  0  0  0  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  X  X  0  0  X  0  X  0  0  0  0  X  X  X  0  X  0  X  0  X  0  X  0  0  X  0  0  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+205x^44+310x^46+514x^48+484x^50+597x^52+472x^54+588x^56+404x^58+299x^60+114x^62+77x^64+8x^66+19x^68+4x^72

The gray image is a linear code over GF(2) with n=106, k=12 and d=44.
This code was found by Heurico 1.16 in 92.5 seconds.