The generator matrix

 1  0  1
 0  1  2
 0  0  X

generates a code of length 3 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+10x^1+47x^2+140x^3+47x^4+10x^5+1x^6

The gray image is a code over GF(2) with n=12, k=8 and d=2.
This code was found by Heurico 1.16 in 5.7e-005 seconds.