The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  1  X  1  1  0  X  1  0  1  1  0  0  0  X  0  X  1  1  0  X  X  X  0  0  1  0  1  X  0  1  X  1  1  1  0  1  1  1  1  1
 0  1  0  0  0  0  0  0  0  1  1  1 X+1  0  1 X+1  X  X  X X+1  X  1 X+1  1  1  1  0  1  1  X X+1  X  1  1  X  0  0  0  X  0  X  0 X+1  1  X  X  0  1  X  X  1  X  X
 0  0  1  0  0  0  1  1  1  X  1 X+1 X+1  0  X  1  0  1  1  0  X  1  0  X  1 X+1  0  0 X+1 X+1  1  1  X X+1  0  1  1  X  1  0  1  X  1  1 X+1  0  X  0  0  0 X+1 X+1 X+1
 0  0  0  1  0  1  1  0 X+1  X  0  X X+1 X+1  X X+1  0  1  X X+1  0  0  0  1  X  1  1 X+1 X+1  0  1  X  X  0  X  1  1  X  0  X  0  1 X+1  0  X X+1  1  1  0  X  1  0  1
 0  0  0  0  1  1  0 X+1 X+1  1  X X+1 X+1  X  1  0  1  0  1  1  1  1  X X+1  X  1 X+1  X  X  X X+1 X+1 X+1 X+1  1  1  X  1  0  1  1  X  1  0  0  X  1  X X+1  0  1 X+1  X
 0  0  0  0  0  X  0  X  X  X  0  X  X  0  X  0  X  0  X  X  X  X  0  X  0  0  0  X  X  X  0  0  0  X  0  0  X  0  X  0  0  X  0  X  0  0  0  X  X  X  X  X  0
 0  0  0  0  0  0  X  0  X  0  X  X  0  X  X  X  0  0  0  X  0  X  0  0  X  0  0  X  X  X  0  0  X  0  X  X  X  0  X  X  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+139x^44+376x^46+544x^48+510x^50+577x^52+496x^54+478x^56+408x^58+287x^60+176x^62+81x^64+18x^66+5x^68

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 1.76 seconds.