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.