The generator matrix

 1  0  1  1  1
 0  1  3  2  0

generates a code of length 5 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+7x^4+6x^6+2x^8

The gray image is a code over GF(2) with n=10, k=4 and d=4.
This code was found by Heurico 1.16 in 3.41e-005 seconds.