The generator matrix
1 0 0 0 1 1 1 X 1 1 0 1 1 0 X 1 1 1 0 X X 0 1 1 1 X 0 1 X 0 1 1 1 0 1 1 1 X 0 X X 0 0 1 X 1 1 X 1 X 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 X 1 1 0 X 0 0 X 1 X 1
0 1 0 0 0 0 0 0 1 1 1 1 X+1 1 1 X 0 1 X 0 1 1 X 1 X+1 1 0 X+1 1 X X+1 X 0 1 1 X X+1 X 1 X 1 0 1 X+1 1 X+1 X 0 X 0 X+1 1 1 X+1 X 0 X 0 0 0 X+1 X X X+1 0 X+1 X 1 0 X X+1 X X 0 X+1 0 1 0 1 1 1 X 1 1
0 0 1 0 0 1 X+1 1 X+1 1 X 0 0 1 1 X 0 X+1 1 X 1 X X+1 0 1 X 1 X X+1 1 0 1 X 1 X 0 1 1 X+1 1 X 0 X X+1 X+1 X+1 0 1 X 1 1 X+1 1 1 1 X+1 X+1 0 0 1 X X+1 0 0 X+1 X+1 1 1 X+1 X X X 1 1 X X 1 1 0 X 0 X+1 X 0
0 0 0 1 1 1 0 1 X X+1 1 1 0 X+1 0 0 X+1 X 0 1 X+1 X 0 0 X+1 1 1 1 0 X X 1 0 0 1 1 X+1 X 1 X+1 1 1 X+1 X 0 X X+1 X+1 0 1 1 X+1 X+1 X 1 1 X 1 0 X 1 X+1 1 X X+1 X+1 X+1 0 1 X X 0 1 X 1 X+1 1 X 0 X 0 0 1 X
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 X 0 0 X X 0 X X X X 0 0 0 X X 0 0 X X X 0 0 X X X X 0 0 0 X X 0 X X 0 0 X 0 X 0 0 X X X X X X X X 0 0 X X 0 X X X X
0 0 0 0 0 X X 0 X X 0 X X 0 0 X X 0 X X X X 0 0 0 X 0 0 X 0 X 0 X 0 X X 0 X X 0 0 X X 0 X X X X X X X 0 X 0 0 0 X 0 X 0 X X X X X 0 0 X X 0 X 0 0 0 X 0 0 X X X 0 X X X
generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 77.
Homogenous weight enumerator: w(x)=1x^0+56x^77+97x^78+102x^79+99x^80+78x^81+74x^82+74x^83+63x^84+50x^85+43x^86+48x^87+38x^88+30x^89+29x^90+10x^91+15x^92+16x^93+26x^94+14x^95+5x^96+22x^97+13x^98+8x^99+2x^100+2x^102+1x^104+2x^105+4x^106+2x^109
The gray image is a linear code over GF(2) with n=168, k=10 and d=77.
This code was found by Heurico 1.16 in 6.56 seconds.