The generator matrix

 1  0  1
 0  1  2
 0  0  X

generates a code of length 3 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+26x^1+271x^2+1452x^3+271x^4+26x^5+1x^6

The gray image is a code over GF(2) with n=24, k=11 and d=4.
This code was found by Heurico 1.16 in 6.87e-008 seconds.