The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  0  X  1  1  1  1  0  1  X  1  0  1  0  X  1  0  1  0  1  0  X  X  1  1  1  1  X  1  1  0  X  0  X  1  1  X  0  0  1  0  X  0  1  X  1  0  X  X  X  X  X  1  1  1  1  X  X  1  1  X  X  0  0  1  X  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  1  X X+1  1  X  X  1  X  X  0  1  1 X+1  0 X+1  1  X  1  0  1  0  X  0 X+1  0 X+1  0  X  0  1  X  1  X  X  1  0  1  1  0  1  X  1  X  1  0  0  0  0  1  0 X+1 X+1 X+1  X  0  X  1  1  0  X  0  0  1  0
 0  0  1  0  0  0  1  1  1  1  X  1  0 X+1 X+1 X+1  X X+1  0  0  X  0  1  1 X+1 X+1  0  1  1  X  0 X+1  X X+1  X  1 X+1  0  1  X  0  1  X  1  1  X  0  1  X  1  1  0  0  X X+1  X  1  0  X  1  0  0  0  1 X+1  1 X+1  1  0  X X+1  X  1  1  1  1  X  0
 0  0  0  1  0  1  1  0  1  0 X+1 X+1  1  X X+1 X+1  X  0  1  1  0  X  0  X  0 X+1 X+1 X+1  1  X  0  0  1 X+1 X+1 X+1  X  0 X+1  0  X  X  0  1  1  1  0  0 X+1  0  X  0  1  0  X  1 X+1 X+1  X  1  1  1  X  0  1 X+1  0  0  1 X+1 X+1 X+1  1  X  0  0  0  0
 0  0  0  0  1  1  0  1  1  X  0  X  1 X+1 X+1  0 X+1  X  0 X+1  0  X  X  1  1 X+1 X+1  X  X X+1  1  0 X+1 X+1  X X+1  X  1  1  0 X+1  1  1 X+1  0  X  X  0  X  0 X+1  X X+1 X+1  X  X  X  0  1  0  1  0 X+1  1  0  X X+1  X  X  0 X+1 X+1  X  1  0  X  1  0
 0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  X  0  0  X  0  X  0  X  0  X  0  0  X  X  X  0  X  0  0  X  0  0  0  0  0  0  0  X  0  X  X  X  0  0  0  X  X  0  0  X  0  X  X  X  X  X  X  X  0  X  0  X  0  0  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  0  0  X  X  X  X  0  0  0  0  X  X  0  X  X  X  0  X  0  0  X  X  X  X  0  X  X  X  X  0  0  0  0  X  0  X  X  X  X  X  0  0  0  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  X  X  0  0  0  0  0  X  0  X  0  X  0  0  0  0  0  X  0  X  0  0  X  X  0  X  X  X  X  X  X  0  0  X  X  X  0  X  0  0  X  0  X  X  0  X  X  0  0  0  0  X  0  0  0  X  0  0  X  0
 0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0  X  0  X  X  0  0  X  0  X  X  X  X  X  X  0  X  X  X  0  X  X  X  X  X  X  X  X  0  0  X  X  0  X  0  0  0  0  0  X  X  0  X  0  X  X  X  0  X  0  X  X  0  0  X  0  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+53x^64+120x^65+204x^66+296x^67+390x^68+442x^69+587x^70+646x^71+718x^72+720x^73+843x^74+876x^75+875x^76+998x^77+876x^78+932x^79+923x^80+954x^81+843x^82+800x^83+725x^84+606x^85+508x^86+414x^87+310x^88+204x^89+181x^90+124x^91+89x^92+50x^93+44x^94+8x^95+10x^96+2x^97+9x^98+1x^100+1x^102+1x^112

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 90.3 seconds.