The generator matrix

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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+12x^49+34x^50+58x^51+48x^52+28x^53+24x^54+20x^55+10x^56+2x^57+1x^64+2x^65+6x^66+2x^67+4x^68+4x^69

The gray image is a linear code over GF(2) with n=106, k=8 and d=49.
This code was found by Heurico 1.10 in 0 seconds.