The generator matrix

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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+54x^45+124x^46+126x^47+131x^48+148x^49+157x^50+152x^51+139x^52+144x^53+132x^54+112x^55+92x^56+94x^57+112x^58+96x^59+64x^60+56x^61+38x^62+26x^63+16x^64+14x^65+11x^66+5x^68+2x^69+2x^70

The gray image is a linear code over GF(2) with n=106, k=11 and d=45.
This code was found by Heurico 1.16 in 1.93 seconds.