The generator matrix

 1  1  2  1  1
 0  2  2  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+9x^2+86x^4+64x^5+86x^6+9x^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 0.000117 seconds.