The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+63x^44+98x^45+128x^46+166x^47+153x^48+142x^49+130x^50+144x^51+122x^52+130x^53+124x^54+120x^55+103x^56+88x^57+102x^58+66x^59+54x^60+48x^61+24x^62+14x^63+15x^64+6x^65+4x^66+2x^67+1x^68

The gray image is a linear code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.10 in 0.156 seconds.