The generator matrix

 1  0  0  1  1
 0  1  0  2  1
 0  0  1  1  3

generates a code of length 5 over Z4 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+8x^3+18x^4+16x^5+8x^6+8x^7+5x^8

The gray image is a code over GF(2) with n=10, k=6 and d=3.
This code was found by Heurico 1.16 in 5.89e-005 seconds.