The generator matrix

 1  0  0  0  1 X^2  X
 0  1  0  0  X  1  1
 0  0  1  0 X+1 X^2+X  X
 0  0  0  1  1 X^2+X X^2

generates a code of length 7 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+178x^4+272x^5+845x^6+1504x^7+845x^8+272x^9+178x^10+1x^14

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^3) for dimension 12.
This code was found by Heurico 1.16 in 0.109 seconds.