The generator matrix

 1  0  1  1  1
 0  1  3  0  0
 0  0  4  0  0
 0  0  0  4  0
 0  0  0  0  4

generates a code of length 5 over Z8 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+17x^2+142x^4+192x^5+142x^6+17x^8+1x^10

The gray image is a code over GF(2) with n=20, k=9 and d=4.
This code was found by Heurico 1.16 in 0.00013 seconds.