The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+14x^4+1x^8

The gray image is a code over GF(2) with n=8, k=4 and d=4.
This code was found by Heurico 1.16 in 5.39e-005 seconds.