The generator matrix

 1  1  1
 0  2  0

generates a code of length 3 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+1x^2+12x^3+1x^4+1x^6

The gray image is a code over GF(2) with n=12, k=4 and d=4.
This code was found by Heurico 1.16 in 3.1e-005 seconds.