The generator matrix

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

generates a code of length 86 over Z2[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+17x^84+36x^85+24x^86+24x^87+11x^88+4x^89+6x^90+1x^96+1x^100+2x^102+1x^104

The gray image is a linear code over GF(2) with n=172, k=7 and d=84.
This code was found by Heurico 1.16 in 0.12 seconds.