The generator matrix

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

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+183x^52+728x^54+1115x^56+1428x^58+1713x^60+1916x^62+2085x^64+2108x^66+1771x^68+1458x^70+1045x^72+486x^74+252x^76+66x^78+26x^80+2x^82+1x^108

The gray image is a linear code over GF(2) with n=128, k=14 and d=52.
This code was found by Heurico 1.16 in 70.5 seconds.