The generator matrix

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

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+32x^2+188x^4+128x^5+480x^6+896x^7+646x^8+896x^9+480x^10+128x^11+188x^12+32x^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 0.013 seconds.