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.