The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  1  X  1  0  X  0  1  X  1  1  1  0  1  1  0  0  X  1  X  1  1  1  0  1  1  1  0  1  1  1  1  1  1  1  0  X  0
 0  1  0  1  0  1  1  0  X  1 X+1  1  1  0  1 X+1  X  1 X+1  X  X  1  X  1  X X+1  1  X  0  1  X  0  1  1  1  1  0  X  0  0  X  0  1  1  0  X X+1  0  0  0  X  0  1
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  1  1  X  X  0  1  1  1  X  X  1  1 X+1 X+1  1  1  1  1  1 X+1 X+1  0  0  1  1  1  X  1  0  1 X+1 X+1  X  0 X+1  0  X  1  0  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  0  0  0  X  X  X  0  0  0  0  X  X  0  0  X  0  X  0  X  X  X  0  X  0  X  X  X  X  0  X  0  X  0  0  X  X  0  0
 0  0  0  0  X  0  0  0  X  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  X  X  0  0  X  X  X  0  X  0  0  X  0  X  0  X  0  0  X  X  X  0  0  0  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  X  0  0  0  X  X  0  0  X  X  X  X  X  X  X  X  0  X  X  X  0  0  0  X  0  X  X  0  X  0  0  0  0  X  0  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  X  X  X  X  0  0  X  0  0  X  X  X  X  0  X  X  0  0  X  X  X  0  0  X  X  0  0  0  0  0  0  X  X  X  0  X  X  0  X  0
 0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  X  0  X  X  X  X  X  X  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  X  0  0  0  X  0  0  0  X  0  X  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+39x^44+62x^45+69x^46+122x^47+145x^48+138x^49+149x^50+140x^51+150x^52+146x^53+122x^54+134x^55+104x^56+106x^57+117x^58+74x^59+57x^60+56x^61+36x^62+40x^63+14x^64+4x^65+13x^66+2x^67+2x^68+4x^70+1x^74+1x^78

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 0.467 seconds.