The generator matrix

 1  1  2  2
 0  4  4  0

generates a code of length 4 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+13x^4+2x^6

The gray image is a code over GF(2) with n=16, k=4 and d=8.
This code was found by Heurico 1.16 in 5.2e-005 seconds.