The generator matrix

 1  0  0  1
 0  1  0  X
 0  0  1  X

generates a code of length 4 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+36x^2+96x^3+246x^4+96x^5+36x^6+1x^8

The gray image is a code over GF(2) with n=16, k=9 and d=4.
This code was found by Heurico 1.13 in 1.07e-007 seconds.