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

generates a code of length 91 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+66x^78+98x^79+191x^80+260x^81+285x^82+346x^83+322x^84+360x^85+372x^86+396x^87+400x^88+424x^89+436x^90+444x^91+451x^92+432x^93+418x^94+354x^95+362x^96+316x^97+251x^98+280x^99+218x^100+174x^101+158x^102+86x^103+88x^104+62x^105+52x^106+42x^107+9x^108+18x^109+10x^110+2x^111+6x^112+2x^113

The gray image is a linear code over GF(2) with n=182, k=13 and d=78.
This code was found by Heurico 1.10 in 4.61 seconds.