The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 X 1 1 1 1 0 1 X 1 1 1 0 1 1 0 1 X 1 1 X 1 0 1 1 1 1 1 1 1 0 1 X 1 1 0 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 X 1 1 1 1 1 0 0 0 0 1 1 0 X 1 0 1 1 X
0 1 1 0 1 1 0 1 1 X X+1 1 1 0 X+1 X+1 0 1 X 1 X+1 X+1 0 1 0 X+1 1 X+1 1 X 0 1 X+1 1 0 X+1 X+1 1 X+1 1 0 1 X 1 0 0 1 1 1 1 X+1 X+1 1 1 X+1 1 X+1 X+1 X+1 1 1 1 X X+1 X+1 1 X+1 X 1 1 1 0 X X 1 X 1 X+1 1 X 1 X 1 X X+1 0
0 0 X 0 0 0 0 0 0 0 X 0 0 X X 0 0 X X X X X X X 0 0 0 0 X X 0 X 0 0 X X X 0 X X 0 0 X X X X X X X 0 0 0 X 0 0 X 0 X X X X X X X 0 0 0 0 X X 0 X X 0 X 0 X 0 0 0 0 X X 0 0 X
0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 0 0 0 X X X X 0 X 0 0 X X X X 0 X 0 X 0 0 0 0 0 X X X X 0 0 0 X 0 0 0 X X 0 0 X X 0 X 0 0 X X 0 X X X 0 0 0 0 0 X X X X X 0 X 0 0 X 0 0
0 0 0 0 X 0 0 0 0 0 X X X 0 0 X X 0 X 0 X X X X X X 0 X X X X X X X 0 X X 0 X 0 X X 0 0 0 X 0 X X X 0 0 0 0 0 X X 0 0 0 0 0 0 X 0 X X X 0 0 0 0 0 0 X 0 X 0 0 0 0 X X 0 0 X
0 0 0 0 0 X 0 0 X 0 0 X 0 0 X X 0 X 0 0 0 X X X 0 X X 0 X 0 X X 0 X X 0 0 0 X 0 0 0 X X 0 0 X X 0 X 0 X 0 0 0 X X 0 X 0 0 X X X 0 X X 0 0 X 0 0 X 0 0 X X 0 X X X X 0 0 0 0
0 0 0 0 0 0 X 0 X X 0 0 X 0 X X X X X X 0 X X X 0 X 0 X X 0 0 0 0 X 0 X 0 X X X 0 0 X X X X 0 0 0 X X X X 0 0 0 0 X 0 0 0 0 0 0 X X 0 X 0 X 0 0 X 0 X 0 0 X 0 0 0 X X 0 X X
0 0 0 0 0 0 0 X X 0 X 0 X 0 0 X 0 X 0 X 0 X 0 0 X X 0 0 0 X X 0 0 0 X X 0 X X 0 X X X X 0 0 0 0 X X 0 X X 0 X 0 X 0 0 X 0 X X X X X 0 0 X 0 0 0 0 X X X X 0 0 0 X 0 0 X X 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+96x^78+161x^80+128x^82+122x^84+101x^86+102x^88+109x^90+76x^92+48x^94+33x^96+16x^98+10x^100+9x^102+4x^104+1x^106+2x^110+1x^112+2x^114+2x^120
The gray image is a linear code over GF(2) with n=172, k=10 and d=78.
This code was found by Heurico 1.16 in 57.8 seconds.