The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 1 X 1 X X 1 1 1 1 0 X 1 X 1 1 1 X 1 1 1 0 X 1 0 1 1 1 X X 0 X X X 1 1 1 1 X 0 X 1 1 1 0 1 X 0 1 0 1 1 0
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 0 1 X+1 0 X X+1 1 0 X 1 1 0 0 X 1 1 X X X 1 1 1 X 0 X 0 X X 1 1 1 0 X 1 1 X X+1 1 1 1 0 0 X+1 1 1 0 1 0 1 0 0 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 0 1 1 X+1 1 1 0 X 0 1 X X 1 0 1 X+1 X 0 X+1 1 0 0 X X+1 0 1 X+1 X X 1 X 0 X+1 X 0 0 1 1 X X 1 X 0 1 0 1 1 1 X+1 0
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 1 0 0 1 0 1 0 0 X+1 1 0 X+1 1 X+1 1 1 1 0 0 X 1 1 X+1 0 X+1 X+1 X X+1 X X 1 0 1 X+1 1 0 X 0 0 X+1 0 0 1 0 X+1 0 1 X+1 1 X X 1
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 X+1 1 1 X 1 X 1 1 X X X+1 X+1 X+1 0 X X+1 1 X+1 X+1 X X+1 0 X 1 1 1 X+1 0 X X+1 X X X X 1 0 X+1 X+1 X+1 X+1 1 X 0 X+1 1 1 1 0 1 X+1 1 0
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X X 0 X 0 X X 0 X 0 X X X X X X 0 X X 0 0 X 0 X X X X 0 0 X 0 X 0 0 0 0 0 0 X 0 X 0 X X X X 0 X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X X 0 0 X X 0 0 X 0 0 X 0 X X 0 X 0 X 0 X 0 X X X 0 X X 0 X 0 X 0 X X X X X X X X X X 0 X X 0 X 0 X 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 X X X X X X X X X X X X X X X 0 X X X X X 0 X 0 X X X X 0 0 0 X X X X X X X X X 0 0 0 0 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+74x^65+152x^66+184x^67+284x^68+318x^69+398x^70+358x^71+371x^72+434x^73+446x^74+498x^75+422x^76+474x^77+473x^78+444x^79+387x^80+388x^81+421x^82+360x^83+290x^84+254x^85+202x^86+170x^87+132x^88+94x^89+74x^90+30x^91+28x^92+10x^93+7x^94+4x^95+4x^96+2x^97+3x^98+1x^104
The gray image is a linear code over GF(2) with n=154, k=13 and d=65.
This code was found by Heurico 1.16 in 13.3 seconds.