The generator matrix

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

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+36x^46+60x^47+82x^48+112x^49+78x^50+92x^51+101x^52+68x^53+52x^54+46x^55+59x^56+48x^57+40x^58+34x^59+19x^60+20x^61+16x^62+22x^63+20x^64+8x^65+2x^66+2x^67+4x^68+2x^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 1.10 in 0.046 seconds.