The generator matrix

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

generates a code of length 90 over Z2[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+50x^77+139x^78+166x^79+288x^80+292x^81+287x^82+320x^83+345x^84+360x^85+409x^86+434x^87+410x^88+468x^89+405x^90+452x^91+447x^92+396x^93+370x^94+374x^95+318x^96+296x^97+279x^98+228x^99+170x^100+132x^101+114x^102+66x^103+50x^104+48x^105+35x^106+8x^107+11x^108+6x^109+7x^110+3x^112+2x^114+3x^116+1x^118+2x^120

The gray image is a linear code over GF(2) with n=180, k=13 and d=77.
This code was found by Heurico 1.16 in 15.6 seconds.