The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1  1  X  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  0  0  1  0  1  X  0  X  0  X  X  0  0  X  X  1
 0  1  1  0  1  1 X+1  0  1  0 X+1  1  X X+1  1  X  1  1  X X+1  1  X  1  1  0 X+1  1  0 X+1  1  0 X+1  1  0 X+1  1  X  1  1  X  1  1  X  1  1  X  1  1  0  0  0  0  0  0  0  0  X  X X+1 X+1 X+1 X+1 X+1 X+1 X+1 X+1  X  1  X  X  X  X  X  0  X  0  X  0  0  X  X  0  0 X+1
 0  0  X  0  0  0  0  X  X  X  X  X  X  0  X  X  0  X  0  X  0  0  X  0  0  0  0  X  X  X  0  0  X  X  X  0  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  X  X  0  X  0  0  X  X  0  X  X  X  X  0  X  X  0  0  0  0
 0  0  0  X  0  X  X  X  X  0  X  0  0  0  0  X  X  X  X  0  X  0  X  0  0  0  X  X  X  0  X  X  X  0  0  0  0  0  0  X  X  X  X  X  X  0  0  0  0  0  X  X  X  X  0  0  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  X  0  X  0  0  X  X  0  0  0  X  X
 0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  X  X  X  0  0  0  0  0  0  X  0  X  0  X  0  X  0  0  0  X  X  0  X  0  0  X  0  X  0  X  X  0  X  0  X  X  0  0  X  X  0  0  X  0  X  X  0  0  X  X  0  X  0  X  0  X  0  0  0  X  X  X  X  0  0  0  X  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+48x^82+39x^84+24x^86+7x^88+6x^90+2x^106+1x^108

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 52.2 seconds.