The generator matrix

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

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

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

The gray image is a code over GF(2) with n=8, k=5 and d=2.
This code was found by Heurico 1.16 in 3.29e-005 seconds.