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

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

Homogenous weight enumerator: w(x)=1x^0+14x^86+32x^87+14x^88+2x^94+1x^96

The gray image is a linear code over GF(2) with n=172, k=6 and d=86.
As d=86 is an upper bound for linear (172,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.144 seconds.