The generator matrix

 1  0  0  0  1
 0  1  0  0  4
 0  0  1  0  0
 0  0  0  1  0
 0  0  0  0  2

generates a code of length 5 over Z8 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+22x^1+205x^2+1096x^3+3634x^4+6468x^5+3634x^6+1096x^7+205x^8+22x^9+1x^10

The gray image is a code over GF(2) with n=20, k=14 and d=2.
This code was found by Heurico 1.16 in 0.0308 seconds.