The generator matrix

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

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+25x^78+60x^79+55x^80+46x^81+51x^82+54x^83+35x^84+28x^85+30x^86+32x^87+22x^88+10x^89+11x^90+8x^91+9x^92+6x^93+2x^94+3x^96+2x^97+6x^98+4x^99+2x^101+3x^102+2x^104+2x^105+2x^107+1x^120

The gray image is a linear code over GF(2) with n=168, k=9 and d=78.
This code was found by Heurico 1.10 in 0.016 seconds.