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
 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
 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
 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

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+13x^82+36x^83+28x^84+24x^85+17x^86+4x^87+1x^96+1x^98+2x^100+1x^102

The gray image is a linear code over GF(2) with n=168, k=7 and d=82.
This code was found by Heurico 1.16 in 0.11 seconds.