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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+47x^68+15x^72+1x^76

The gray image is a linear code over GF(2) with n=136, k=6 and d=68.
As d=68 is an upper bound for linear (136,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0786 seconds.