The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  0  X  1  0  X  1  1  1  0  X  0  X  0
 0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  0  X  X  X  X  X  X  0  0  0  0  0  X  X  X  X  0  0  0  0  0  0  0  X  X  X  X  0  0  0  0  0  0  X  X  0  X  X  X  X
 0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  X  X  X  X  0  0  0  X  X  0  X  X  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  X  0  X  0  X  X  X  X  0  X  X  X  0  0  0  0  0
 0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  0  0  X  X  0  X  X  0  0  0  X  X  0  0  X  X  X  0  0  X  X  X  X  0  0  X  X  0  0  0  X  X  0  X  X  0  X  0  X  0  0  0  0  X  0  X  X  0  0
 0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  0  X  0  X  X  0  X  X  X  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+52x^84+6x^88+5x^96

The gray image is a linear code over GF(2) with n=168, k=6 and d=84.
As d=84 is an upper bound for linear (168,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 4.15 seconds.