The generator matrix

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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+69x^64+56x^65+139x^66+192x^67+242x^68+308x^69+353x^70+320x^71+409x^72+446x^73+409x^74+430x^75+508x^76+500x^77+452x^78+568x^79+353x^80+444x^81+392x^82+356x^83+308x^84+228x^85+200x^86+152x^87+115x^88+62x^89+74x^90+30x^91+28x^92+4x^93+16x^94+13x^96+9x^98+2x^100+3x^102+1x^106

The gray image is a linear code over GF(2) with n=154, k=13 and d=64.
This code was found by Heurico 1.16 in 13.3 seconds.