The generator matrix

 1  1
 0 2X

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

Homogenous weight enumerator: w(x)=1x^0+30x^2+1x^4

The gray image is a code over GF(2) with n=16, k=5 and d=8.
This code was found by Heurico 1.16 in 1.05e-007 seconds.