The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+46x^2+296x^4+946x^6+1518x^8+946x^10+296x^12+46x^14+1x^16

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^2) for dimension 12.
This code was found by Heurico 1.16 in 0.0125 seconds.