The generator matrix

 1  1
 0 X+2

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

Homogenous weight enumerator: w(x)=1x^0+4x^1+22x^2+4x^3+1x^4

The gray image is a code over GF(2) with n=8, k=5 and d=2.
This code was found by Heurico 1.16 in 0.462 seconds.