The generator matrix

 1  0  1  X  1  1
 0  1  X  1 X+1  1

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

Homogenous weight enumerator: w(x)=1x^0+12x^6+3x^8

The gray image is a linear code over GF(2) with n=12, k=4 and d=6.
As d=6 is an upper bound for linear (12,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 7.2e-005 seconds.