The generator matrix

 1  1
 0  2

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

Homogenous weight enumerator: w(x)=1x^0+14x^2+1x^4

The gray image is a code over GF(2) with n=8, k=4 and d=4.
This code was found by Heurico 1.16 in 1.81e-005 seconds.