The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 X 0 0 X X 0 0 X X
0 0 X 0 0 X 0 X X 0 X X X X
0 0 0 X 0 X X X 0 0 X 0 0 X
0 0 0 0 X X X 0 0 X X X X X
generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+15x^12+32x^14+15x^16+1x^28
The gray image is a linear code over GF(2) with n=28, k=6 and d=12.
As d=12 is an upper bound for linear (28,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.00066 seconds.