The generator matrix

 1  0  1
 0  1  2

generates a code of length 3 over Z4 who´s minimum homogenous weight is 2.

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

The gray image is a code over GF(2) with n=6, k=4 and d=2.
This code was found by Heurico 1.16 in 1.81e-005 seconds.