The generator matrix

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

generates a code of length 7 over Z2[X]/(X^2) who�s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+47x^2+40x^3+301x^4+480x^5+675x^6+1008x^7+675x^8+480x^9+301x^10+40x^11+47x^12+1x^14

The gray image is a linear code over GF(2) with n=14, k=12 and d=2.
As d=2 is an upper bound for linear (14,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.16 in 0.0129 seconds.