The generator matrix
1 0 0 0 1 1 1 1 X 1 1 X 1 0 1 X 1 0 0 X 1 X 0 X X 0 1 1 0 0 1 1 1 1 1 0 1 X 1 1 0 X 1 1 1 1 1 1 X 1 1 1 1
0 1 0 0 0 1 X 0 0 1 1 1 X+1 1 1 1 0 0 X 1 X 1 X 0 X 1 1 X 0 1 X+1 1 X 0 1 1 0 1 X+1 1 X 1 0 1 0 1 X+1 X+1 1 1 X+1 X+1 1
0 0 1 0 1 1 1 X 1 X 0 0 1 1 0 X+1 X 1 1 0 1 1 X 1 1 X+1 0 X+1 X X 0 1 X 0 1 0 1 0 1 X X 0 1 X X 1 X+1 1 1 X+1 X 0 1
0 0 0 1 1 0 0 1 1 X+1 X X+1 1 1 X 0 X X+1 0 1 X+1 X+1 1 X 1 0 X 0 1 X X+1 0 1 0 X X+1 X+1 X+1 1 X+1 1 X X X X X+1 0 X X 1 0 X+1 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X 0 X X X X 0 0 X 0 X X X X X X X X X 0 X 0 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 X X X 0 X X X X X X X X 0 0 X X 0 X 0 X 0 X 0 X X X X X 0 0 0 0 X 0 0 0 0 X 0 X 0
generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.
Homogenous weight enumerator: w(x)=1x^0+24x^46+72x^47+88x^48+94x^49+99x^50+106x^51+76x^52+56x^53+70x^54+46x^55+47x^56+48x^57+42x^58+42x^59+30x^60+16x^61+14x^62+18x^63+9x^64+10x^65+7x^66+4x^67+2x^68+3x^72
The gray image is a linear code over GF(2) with n=106, k=10 and d=46.
This code was found by Heurico 1.16 in 0.122 seconds.