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  8

generates a code of length 5 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+285x^2+3360x^3+24930x^4+73920x^5+24930x^6+3360x^7+285x^8+1x^10

The gray image is a code over GF(2) with n=40, k=17 and d=8.
This code was found by Heurico 1.16 in 2.16 seconds.