The generator matrix
1 0 0 1 1 1 X 1 0 1 1 1 X 0
0 1 0 0 1 X+1 1 X X 0 X+1 X+1 1 1
0 0 1 1 X+1 0 X+1 1 1 X X+1 X X+1 0
0 0 0 X X X 0 0 X 0 0 X X 0
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+70x^12+47x^16+10x^20
The gray image is a linear code over GF(2) with n=28, k=7 and d=12.
As d=12 is an upper bound for linear (28,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.00312 seconds.