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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+48x^66+39x^68+24x^70+7x^72+4x^74+1x^76+4x^82

The gray image is a linear code over GF(2) with n=136, k=7 and d=66.
As d=66 is an upper bound for linear (136,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 77.5 seconds.