The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  0  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  0  1  1 X+1  0  1  0 X+1  1  0 X+1  1  0  1  1  0 X+1  1  0  1  1  X X+1  1  X X+1  1  X X+1  1  X X+1  1  X  1  1  X  1  1  X  1  1  X  1  1  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0 X+1  0 X+1  1  1  0 X+1  0 X+1  X  1  X  1  X X+1  0  0  X  1  1 X+1
 0  0  X  0  0  0  0  X  X  X  X  X  0  0  0  X  X  X  0  X  0  X  0  X  X  0  X  X  0  X  0  X  0  0  X  0  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  0  0  0  0  0  X  X  X  0  0  X  X  0  0  0  0  X  0  X  X  X  X  0
 0  0  0  X  0  X  X  X  X  0  X  0  0  0  X  X  X  0  X  0  0  0  X  X  0  0  0  X  X  X  X  X  X  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  X  X  0  X  X  X  X  0  X  X  X  0  0  X  0
 0  0  0  0  X  0  X  X  X  X  0  X  X  0  X  0  X  0  X  X  X  0  0  0  0  X  0  X  0  X  0  X  0  X  0  X  X  X  X  0  0  0  X  X  X  0  0  0  X  X  0  0  X  X  0  0  X  X  X  0  0  X  0  0  X  X  0  0  X  0  X  0  X  0  X  X  X  0  0  0  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+58x^82+25x^84+30x^86+2x^88+2x^90+3x^92+2x^94+4x^98+1x^104

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 0.094 seconds.