The generator matrix

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

generates a code of length 5 over Z16 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+30x^1+365x^2+2280x^3+7570x^4+45044x^5+7570x^6+2280x^7+365x^8+30x^9+1x^10

The gray image is a code over GF(2) with n=40, k=16 and d=4.
This code was found by Heurico 1.16 in 0.197 seconds.