The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+16x^78+48x^79+82x^80+104x^81+106x^82+98x^83+76x^84+52x^85+50x^86+50x^87+49x^88+48x^89+36x^90+34x^91+26x^92+16x^93+19x^94+34x^95+14x^96+8x^97+10x^98+6x^99+6x^100+4x^101+11x^102+8x^105+6x^106+2x^107+2x^108+2x^110

The gray image is a linear code over GF(2) with n=172, k=10 and d=78.
This code was found by Heurico 1.10 in 0.094 seconds.