The generator matrix

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

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+52x^45+104x^46+128x^47+151x^48+182x^49+165x^50+112x^51+157x^52+130x^53+105x^54+126x^55+97x^56+104x^57+81x^58+86x^59+83x^60+64x^61+47x^62+26x^63+23x^64+10x^65+10x^66+2x^67+2x^69

The gray image is a linear code over GF(2) with n=106, k=11 and d=45.
This code was found by Heurico 1.10 in 0.156 seconds.