The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+4x^2+22x^4+4x^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.