The generator matrix

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

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+82x^66+94x^68+26x^70+25x^72+8x^74+2x^78+1x^80+10x^82+6x^84+1x^88

The gray image is a linear code over GF(2) with n=138, k=8 and d=66.
As d=66 is an upper bound for linear (138,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 0.0969 seconds.