The generator matrix

 1  0  1
 0  1 X+1
 0  0 2X

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

Homogenous weight enumerator: w(x)=1x^0+87x^2+336x^3+87x^4+1x^6

The gray image is a code over GF(2) with n=24, k=9 and d=8.
This code was found by Heurico 1.16 in 3.81e-009 seconds.