The generator matrix

 1  1  2  1  1
 0  2  2  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+7x^2+40x^4+32x^5+40x^6+7x^8+1x^10

The gray image is a code over GF(2) with n=20, k=7 and d=4.
This code was found by Heurico 1.16 in 8.42e-005 seconds.