The generator matrix

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

generates a code of length 6 over Z2[X]/(X^2) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+18x^2+111x^4+252x^6+111x^8+18x^10+1x^12

The gray image is a linear code over GF(2) with n=12, k=9 and d=2.
As d=2 is an upper bound for linear (12,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9.
This code was found by Heurico 1.16 in 6.87e-008 seconds.