The generator matrix

 1  0  0  1  1  1  0  1  1  0  1  1  X  X
 0  1  0  0  1  1  1  0  0  X  1  1  1  1
 0  0  1  1  1  0  1  0  1  1  1  X  0  1
 0  0  0  X  0  0  0  0  0  X  0  X  X  0
 0  0  0  0  X  0  0  0  0  0  0  X  X  X
 0  0  0  0  0  X  0  0  0  0  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  X  0  X  0  X
 0  0  0  0  0  0  0  0  X  X  X  0  0  X

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+125x^8+384x^10+888x^12+1280x^14+923x^16+384x^18+104x^20+7x^24

The gray image is a linear code over GF(2) with n=28, k=12 and d=8.
As d=8 is an upper bound for linear (28,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.16 in 0.0845 seconds.