The generator matrix

 1  0  0  0  1
 0  1  0  0  3
 0  0  1  0  1
 0  0  0  1  1
 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+125x^2+480x^3+2050x^4+2880x^5+2050x^6+480x^7+125x^8+1x^10

The gray image is a code over GF(2) with n=20, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0106 seconds.