The generator matrix

 1  0  0  0  1
 0  1  0  0  1
 0  0  1  0  1
 0  0  0  1  1

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

Homogenous weight enumerator: w(x)=1x^0+60x^2+240x^3+1030x^4+1440x^5+1020x^6+240x^7+65x^8

The gray image is a code over GF(2) with n=20, k=12 and d=4.
This code was found by Heurico 1.11 in 0.000177 seconds.