The generator matrix

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

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+240x^64+292x^66+815x^68+852x^70+1516x^72+1458x^74+2018x^76+1886x^78+2168x^80+1592x^82+1439x^84+848x^86+724x^88+210x^90+227x^92+30x^94+51x^96+10x^100+4x^104+3x^108

The gray image is a linear code over GF(2) with n=156, k=14 and d=64.
This code was found by Heurico 1.16 in 61 seconds.