The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  X  1  1  1  1  X  0  X  1  1  0  0  0  1  0  1  0  0  1  1  1  0  1  0  1  1  1  X  0  1  1  X  1  X  X  1  0  1  X  0  X  1  1  X  1  X  X  1  1  1  1  1  0  1  1  X  1  X  1  1  1  1  1  1  1
 0  1  0  1  0  1  1  0  0  1 X+1  1  X  1  0  X  1 X+1  1  1  X  0 X+1  1  0  X  1  1  0  1  1  1  X  0  1  1  X  0 X+1  1  1  1  X  X  1  1  1  1  X  X  X  1  0  1 X+1  X  X  1  1  1  1  X  0  X  X  1  1 X+1  1  X  1  1 X+1  1  X  X  X  0
 0  0  1  1  1  0  1  0  1  1  0  X  1 X+1 X+1  X X+1  0  1  0  1  0  X X+1  1  1  1  X  0  1 X+1  X  1  X  0  X  1  0 X+1  X  X  X X+1 X+1  X  1  1  X  0  1  1  1  1 X+1 X+1 X+1  1  X  0  X  X  0  X X+1  1  X  1  1  0  X X+1 X+1 X+1  0 X+1 X+1  1  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  0  0  0  X  0  X  X  0  X  X  0  0  X  0  0  0  0  X  X  0  X  0  X  0  X  X  X  0  0  X  X  0  0  0  0  X  0  X  0  X  X  X  X  X  X  0  0  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  X  0  0  X  0  X  X  X  X  0  0  0  0  X  X  0  0  0  X  X  X  X  X  0  X  X  X  X  X  X  X  0  0  X  0  X  0  X  X  X  X  0  X  0  X  X  0  0  X  0  0  X  X  0  X  X  X  0  X  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  X  X  X  X  0  X  0  X  X  X  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  X  0  X  0  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  0  X  0  X  0  0  X  0  0  X  X  0  X  X  0  0  0  X  X  X  X  0  X  0  0  X  X  X  0  X  X  0  0  X  0  X  X  X  X  X  X  0  0  0  X  0  0  0  X  0  X  X  X  0  0  0  0  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  X  0  X  0  0  X  0  X  X  0  X  X  0  0  X  0  X  0  0  0  X  0  0  X  0  X  X  0  X  0  X  0  X  0  X  0  X  X  0  X  X  0  X  0  0  X  0  0  X  X  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  0  X  X  X  0  0  0  X  X  X  0  X  0  0  0  X  X  X  0  0  0  0  0  0  X  X  0  X  X  X  X  0  X  0  0  X  0  0  X  X  X  0  0  X  X  X  X  X  X  0  X  0  0  X  X  X  X  X  0  0  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  X  X  0  0  0  0  X  0  X  X  0  0  X  X  0  0  X  X  X  X  0  0  X  0  0  X  X  X  0  0  X  X  X  X  X  X  0  X  X  X  0  0  X  X  X  0  0  X  0  0  X  0  0  0  X  X  0  0  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+28x^64+36x^65+89x^66+142x^67+210x^68+222x^69+288x^70+272x^71+365x^72+420x^73+441x^74+472x^75+431x^76+466x^77+450x^78+518x^79+454x^80+476x^81+431x^82+414x^83+329x^84+290x^85+238x^86+188x^87+156x^88+124x^89+83x^90+28x^91+49x^92+14x^93+14x^94+14x^95+17x^96+12x^98+5x^100+2x^102+3x^104

The gray image is a linear code over GF(2) with n=156, k=13 and d=64.
This code was found by Heurico 1.16 in 13.3 seconds.