The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  1  X  1
 0  1  1  0 X+1  1  X X+1  1  X  0  X  0  0
 0  0  X  0  X  0  0  X  0  0  X  X  X  0
 0  0  0  X  X  X  X  0  X  0  0  0  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+21x^12+24x^14+14x^16+3x^20+1x^24

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 0.000597 seconds.