The generator matrix

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

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+9x^68+18x^69+13x^70+12x^71+6x^72+2x^73+3x^74

The gray image is a linear code over GF(2) with n=138, k=6 and d=68.
As d=68 is an upper bound for linear (138,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0488 seconds.