The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+86x^43+133x^44+200x^45+271x^46+208x^47+247x^48+314x^49+230x^50+226x^51+294x^52+306x^53+306x^54+210x^55+223x^56+214x^57+152x^58+140x^59+109x^60+110x^61+55x^62+22x^63+16x^64+8x^65+10x^66+4x^67+1x^72

The gray image is a linear code over GF(2) with n=104, k=12 and d=43.
This code was found by Heurico 1.16 in 60 seconds.