The generator matrix

 1  1
 0  3

generates a code of length 2 over Z4 who´s minimum homogenous weight is 1.

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

The gray image is a code over GF(2) with n=4, k=4 and d=1.
This code was found by Heurico 1.16 in 5.51e-005 seconds.