The generator matrix

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

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+67x^44+94x^45+124x^46+180x^47+139x^48+136x^49+139x^50+144x^51+128x^52+124x^53+131x^54+100x^55+112x^56+108x^57+84x^58+72x^59+53x^60+46x^61+24x^62+16x^63+12x^64+4x^65+9x^66+1x^70

The gray image is a linear code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.16 in 0.444 seconds.