The generator matrix

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

generates a code of length 4 over Z2[X]/(X^3) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+24x^1+220x^2+936x^3+1734x^4+936x^5+220x^6+24x^7+1x^8

The gray image is a linear code over GF(2) with n=16, k=12 and d=2.
As d=2 is an upper bound for linear (16,12,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 12.
This code was found by Heurico 1.16 in 0.00164 seconds.