The generator matrix

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

generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+224x^52+682x^54+1097x^56+1392x^58+1772x^60+1914x^62+2070x^64+2074x^66+1948x^68+1398x^70+958x^72+508x^74+221x^76+86x^78+25x^80+10x^82+2x^84+1x^92+1x^104

The gray image is a linear code over GF(2) with n=128, k=14 and d=52.
This code was found by Heurico 1.10 in 11.4 seconds.