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.