The generator matrix

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

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+64x^77+112x^78+90x^79+47x^80+88x^81+126x^82+74x^83+29x^84+42x^85+58x^86+42x^87+40x^88+36x^89+46x^90+24x^91+8x^92+10x^93+22x^94+14x^95+8x^97+12x^98+6x^99+3x^100+2x^101+8x^102+6x^103+4x^105+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 0.319 seconds.