The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  0  1  1  1  1  0  1  X  1  X  1  0  X  X  1  1  X  0  1  1  1  1  X  X  0  1  1  X  1  1  X  1  1  1  0  1  X  X  1  X  1  X  X  0  0  X  X  1  X  X  1  1  0  X  X  1  X  1  0  1  X  1  0  X
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  1  X  1  X X+1  0  1  1  0  1  X  X  0  1  1  X X+1  1  0  1  X  0  X  1  X  1  1  X  1  1  1  1  1  0  X  X  1  X  X  1  1  0 X+1  1  0  1  1  1  1  X  0  1 X+1  1  X  1  1  0  X X+1  1 X+1  1  X  1  0
 0  0  1  0  1  1  0  1  0  1  1  0  0  1 X+1 X+1  X  0  1 X+1 X+1  X  0  1  0  X  X  0  0  1  1  X  1  1  1  X  1  1 X+1  X  1  1  1  X  1 X+1  0  0  X  X  X  1  X  1  1  1  1  0 X+1  X  1  X  1  0  1  X  0  0  0  X  1  0  1  0  0  1  X  0
 0  0  0  1  1  0  1  1  1  0  1  X  1  1  0  X  1 X+1  X X+1  1  1  0  0 X+1  X  0  1  1  0  0  X  0 X+1 X+1  0  1  X  0  0 X+1  0  X X+1  1  0  0  0 X+1 X+1  1  1 X+1  1  0  1  1  X  1  1 X+1 X+1  X X+1 X+1  X  1  X  X  1  1  0  1  X X+1  X  1  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  X  X  0  X  0  0  X  0  X  0  0  X  X  0  0  X  X  X  0  0  0  0  X  0  X  X  X  X  X  0  0  X  0  X  X  X  X  X  X  0  0  X  X  0  0  0  X  0  X  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  X  0  X  0  X  X  X  X  X  0  X  X  X  X  0  X  X  0  0  0  0  X  X  X  0  X  X  X  X  0  0  0  0  X  0  X  0  0  X  0  0  0  X  0  X  X  0  X  0  X  X  X  0  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  X  0  X  0  X  X  X  X  X  0  X  0  X  X  0  0  0  0  X
 0  0  0  0  0  0  0  X  0  0  X  X  0  0  X  0  0  X  X  0  X  0  0  X  0  X  X  0  X  X  X  X  0  X  0  0  X  0  0  0  X  0  0  X  X  X  X  0  0  0  X  X  0  0  0  X  X  0  0  X  0  0  X  X  X  0  X  X  0  X  X  X  X  0  X  0  0  0
 0  0  0  0  0  0  0  0  X  0  X  0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  0  X  X  X  0  0  0  X  0  X  X  X  0  0  X  X  0  X  0  X  0  X  0  0  0  X  X  X  0  0  X  0  X  0  X  X  X  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  0  0  X  0  X  X  X  X  0  X  X  X  0  0  X  X  0  X  0  0  X  0  0  0  0  X  0  0  0  X  0  0  X  0  X  0  X  X  X  X  0  X  0  0  X  0  0  0  X  0  0  0  X  0  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+128x^64+405x^66+805x^68+1082x^70+1315x^72+1652x^74+1845x^76+1870x^78+1906x^80+1754x^82+1390x^84+986x^86+632x^88+364x^90+147x^92+58x^94+17x^96+17x^98+4x^100+4x^102+1x^104+1x^116

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 47.1 seconds.