The generator matrix

 1  0  1
 0  1  2
 0  0 X^2

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

Homogenous weight enumerator: w(x)=1x^0+18x^1+111x^2+764x^3+111x^4+18x^5+1x^6

The gray image is a code over GF(2) with n=24, k=10 and d=4.
This code was found by Heurico 1.16 in -6.48e-008 seconds.