The generator matrix

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

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+90x^43+155x^44+180x^45+236x^46+232x^47+259x^48+280x^49+250x^50+264x^51+314x^52+278x^53+198x^54+242x^55+288x^56+198x^57+159x^58+164x^59+113x^60+78x^61+46x^62+30x^63+20x^64+10x^65+6x^66+2x^67+2x^68+1x^74

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 2.73 seconds.