The generator matrix

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

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+125x^4+384x^5+888x^6+1280x^7+923x^8+384x^9+104x^10+7x^12

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 0.00773 seconds.