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.