The generator matrix

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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+52x^65+128x^66+224x^67+286x^68+336x^69+380x^70+374x^71+402x^72+440x^73+449x^74+416x^75+459x^76+472x^77+446x^78+454x^79+403x^80+420x^81+364x^82+310x^83+347x^84+284x^85+213x^86+156x^87+115x^88+88x^89+62x^90+42x^91+32x^92+20x^93+5x^94+8x^95+3x^96+1x^98

The gray image is a linear code over GF(2) with n=154, k=13 and d=65.
This code was found by Heurico 1.10 in 3.8 seconds.