The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  X  1  1  1  X  1  X  1  0  1  X  0  1  X  X  1  X  1  1  X  1  1  1  0  X  X  1  0  0  1  1  1  1  1  0  1  1  0  1  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  X  1 X+1  1  1  1 X+1  1 X+1  X  1  X  1  1 X+1  1  0 X+1  X  0  1  X  X  1  X  1  X  0  1 X+1  1 X+1  1  1  X  0  1  X  1  0  0
 0  0  1  0  0  0  0  0  X  X  1  1 X+1  0  0  X X+1 X+1 X+1 X+1  0  1  X X+1  0  1 X+1 X+1 X+1  X  1 X+1  1  X  1  0  1  1  X  1 X+1  1  0 X+1  1 X+1 X+1  1  0 X+1  1  0  0
 0  0  0  1  0  0  X  1 X+1  1  0  1  1  0 X+1  1  X X+1  0 X+1  1  1  0  X  1  0 X+1  0 X+1  0  X  X  1  0  X  X  X X+1  1  1  1  1  0  1  0  0  0  1 X+1  X  X  X  X
 0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  X  1  1  0  X  1  1  0  0  1 X+1  X  1  X  0  X X+1  1 X+1  1  X  0  1  X  0  1  1  1  1  0  X  X  1  X  X  1  1  0  X X+1
 0  0  0  0  0  1  1  X  1  1 X+1  X  1  1 X+1  0  0  0  1  1  X X+1 X+1  X X+1  X X+1  1  X  0  1  X  X X+1 X+1  X X+1  0  0 X+1 X+1  0  X  0  X  X  1  1  0  X  X  X  1

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+163x^44+420x^46+499x^48+506x^50+502x^52+486x^54+525x^56+428x^58+306x^60+154x^62+79x^64+22x^66+4x^68+1x^84

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 1.71 seconds.