The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  1  X  1  0  1  1  X  1  1  X  0  0  1  X  1  1  1  1  0  0  X  1  X  1  X  X  1  0  0  1  1  1  1  1  1  1  X  0  1  1  0  X  X  1  1  1  1  1  1  1  0  1  X
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  1  1  1  1 X+1  1  1  1  1  X  0  X X+1 X+1  X  X  1  1  1 X+1  X  1  X  1  1 X+1  1  1  1  0  1 X+1  1  1  0  0  1  X  0  X X+1  X  X  X  X  1  1  X  1
 0  0  1  0  0  0  0  0  0  0  1  1  1 X+1  1  X  1 X+1  0  0 X+1 X+1  X X+1  1  X  1  1  X  X  0  0  1  0  1  1  X  0 X+1 X+1 X+1  1 X+1  X  X  X  1 X+1  X  1  X  X  0  X X+1  1 X+1  0  1 X+1  0 X+1  1  X
 0  0  0  1  0  0  0  1  1  1  X  1 X+1 X+1 X+1  X  0  0  X X+1 X+1  0  1 X+1  X  X  0  0 X+1  X  1  X X+1 X+1 X+1  X  X  1  X  0  X  0  X  1  1 X+1 X+1 X+1  0 X+1  0  1  1  1  0  1  1 X+1  1 X+1 X+1  0  0 X+1
 0  0  0  0  1  0  1  1  0 X+1  X  0  X X+1  1  0 X+1 X+1 X+1  1  X  X  X  1 X+1  0 X+1  0  X  1  0 X+1  0 X+1 X+1  1  1  X  1  0  1  0  X  X  X X+1 X+1 X+1 X+1  1 X+1  1  0 X+1  0 X+1  X  0  1  0 X+1 X+1  0  1
 0  0  0  0  0  1  1  0 X+1 X+1  1  X X+1 X+1  X  1 X+1  0  0 X+1  X  1 X+1  0  1  X  X  X  X  0  0 X+1  1  0  0  X  0  X X+1  0  X X+1  1 X+1  X  X  1  0  0  X  0  X X+1  1  0  1  1  1  1 X+1  1  X X+1  1
 0  0  0  0  0  0  X  0  X  X  X  0  X  X  0  X  X  0  0  X  0  X  X  0  X  0  0  X  X  X  X  0  0  X  X  X  X  0  0  0  X  X  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  0  X  0  X
 0  0  0  0  0  0  0  X  0  X  0  X  X  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  X  X  0  X  X  0  0  0  0  X  X  X  X  0  0  X  0  0  X  X  0  0  X  0  X  0  0  0  X  X  X  0  X  0  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+247x^52+654x^54+1065x^56+1444x^58+1744x^60+1988x^62+2040x^64+2028x^66+1872x^68+1442x^70+1015x^72+552x^74+179x^76+76x^78+23x^80+8x^82+5x^84+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 70.6 seconds.