The generator matrix
1 0 0 1 1 1 0 1 1 X 1 X 1 X 1 1 0 1 X 0 1 0 1 X 1 X 1 0 1 1 X 1 1 0 1 X 1 0 1 X 1 0 1 X 1 1 0 1 1 X 1 X 1 0 0 X 0 1 0 1 X X 0 0 1 0 1 X X
0 1 0 0 1 1 1 X X+1 1 0 0 X+1 1 0 X X 1 1 1 X 1 X 1 X+1 X 0 1 1 X 1 X+1 0 1 X 1 0 1 X 1 0 1 X 1 1 1 X 1 1 0 X+1 0 0 X 1 0 X 1 X 0 X X 0 0 X+1 0 X+1 X 1
0 0 1 1 X X+1 1 0 X 0 X+1 1 1 1 0 1 1 1 0 X+1 0 0 X+1 X+1 X+1 1 1 1 X X+1 X+1 0 X+1 X+1 1 1 X X X X X X X X 0 1 1 0 X+1 1 0 0 0 0 X X X 1 1 1 0 X X 0 1 1 X+1 1 X+1
0 0 0 X 0 X X X X X 0 X 0 0 X 0 X X 0 0 0 X X X 0 0 0 0 X 0 0 X X X X X 0 0 0 0 X X X X 0 0 0 X 0 0 0 X 0 X 0 X X 0 0 0 X X X X X X X X 0
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+88x^68+32x^72+4x^76+3x^80
The gray image is a linear code over GF(2) with n=138, k=7 and d=68.
As d=68 is an upper bound for linear (138,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.10 in 542 seconds.