The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 1 1 1 1 X 1 X 1 X 1 1 X 0 X X X 1 1 0 0 1 1 1 X 0 0 1 0 1 0 0 1 X 0 X 0 X X
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 X+1 1 X+1 1 X+1 X X 1 X+1 1 1 1 X 1 1 1 0 0 1 X+1 X+1 X+1 1 1 1 1 X X X 0 1 1 0 X 1 0 X
0 0 1 0 0 0 0 0 X X 1 1 1 X 0 0 X+1 X+1 X+1 1 1 1 1 X X+1 X 1 1 1 X 0 X+1 1 X 1 0 0 1 X+1 X+1 X+1 0 1 X X 1 1 X 0 1 1 1
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X X+1 X+1 0 0 1 1 X X X 0 1 X+1 0 1 X X+1 1 X+1 1 1 X+1 1 X X+1 1 X 0 X 1 0 0 X+1 1 1 X+1 X+1 0
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 0 X 1 1 0 X+1 X 1 X+1 X X+1 X+1 X 1 X X 1 X X+1 X+1 0 0 1 0 X+1 0 0 1 1 0 1 X 1 1 X+1 1
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 1 X 0 0 1 X 1 X X+1 1 1 1 0 1 0 0 X+1 0 X+1 0 1 1 0 1 X 1 X+1 X+1 1 X+1 X+1 X+1 0 1 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+100x^43+140x^44+188x^45+247x^46+220x^47+279x^48+236x^49+266x^50+266x^51+244x^52+308x^53+272x^54+272x^55+226x^56+212x^57+176x^58+128x^59+120x^60+64x^61+56x^62+36x^63+14x^64+16x^65+6x^66+2x^67+1x^78

The gray image is a linear code over GF(2) with n=104, k=12 and d=43.
This code was found by Heurico 1.10 in 4.19 seconds.