The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+15x^2+64x^4+96x^5+64x^6+15x^8+1x^10

The gray image is a code over GF(2) with n=20, k=8 and d=4.
This code was found by Heurico 1.16 in 6.79e-005 seconds.