The generator matrix

 1  0  0  1
 0  1  0  2
 0  0  1  2

generates a code of length 4 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+8x^2+16x^3+14x^4+16x^5+8x^6+1x^8

The gray image is a code over GF(2) with n=8, k=6 and d=2.
This code was found by Heurico 1.16 in 3.1e-005 seconds.