The generator matrix

1 0 0 0 0 1 1 1 0 0 X 1 1 X 1 1 1 1 X 1 0 1 X 1 1 0 0 1 1 1 X X 1 1 1 0 1 0 X X 0 X 1 0 1 X 0 1 0 1 1 0 0 1 X 1 X 1 0 X 1 X 1 1 X X 1 0 X 0 1 X 1 1 1 1 1 0 0 X 1 X 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 X 1 X+1 1 1 1 X+1 1 X+1 1 1 1 1 X+1 X 1 1 X 1 X+1 X X 0 X 1 X 1 0 1 X X 1 X 1 X X 1 X X+1 1 0 0 X+1 X 1 1 1 X+1 X+1 X 1 X 1 1 1 X+1 0 X+1 X 1 X 1 1 0 X X+1 0 0 0
0 0 1 0 0 0 1 1 1 X 1 1 0 1 0 1 1 X X+1 X X+1 0 1 X+1 0 X X+1 X+1 X+1 X+1 X+1 X X+1 0 X+1 0 X X 1 X 1 0 X X 0 1 1 X 0 1 X 0 1 0 X+1 X 1 X 1 X X+1 X X+1 X 0 1 0 X+1 1 1 0 X X+1 0 1 X+1 X 1 X 0 1 X 0 1
0 0 0 1 0 1 X X+1 1 1 0 0 X X+1 X+1 X+1 1 X X+1 X+1 X 0 1 1 1 1 0 0 X 1 X+1 0 X+1 X+1 X+1 1 0 1 X+1 1 X 0 X+1 X+1 X 0 X X 1 0 1 0 0 0 X 0 1 1 X 0 1 X 0 X X X+1 X+1 1 X 0 1 1 X 1 X+1 0 1 X 1 1 X X X 0
0 0 0 0 1 X 0 X X 1 1 X+1 1 X+1 X+1 X+1 1 X+1 0 X X+1 X X+1 0 X+1 X X X+1 X 1 X 1 X X X+1 X X X+1 0 X+1 X+1 X+1 X+1 X X+1 X X X+1 1 X+1 X X X X+1 1 X 1 1 1 X X 0 X X 1 X 1 1 0 X+1 X X X+1 1 X X+1 0 X+1 0 X X 1 0 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+66x^77+117x^78+82x^79+48x^80+80x^81+117x^82+80x^83+40x^84+40x^85+77x^86+44x^87+21x^88+44x^89+25x^90+34x^91+11x^92+12x^93+26x^94+4x^95+4x^96+10x^97+12x^98+6x^99+1x^100+2x^101+6x^102+6x^103+2x^104+2x^105+2x^106+2x^110

The gray image is a linear code over GF(2) with n=168, k=10 and d=77.
This code was found by Heurico 1.10 in 0.187 seconds.