The generator matrix

 1  0  0  1  1
 0  1  0  0  8
 0  0  1  0  0
 0  0  0 12  0
 0  0  0  0  4

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

Homogenous weight enumerator: w(x)=1x^0+34x^1+381x^2+1848x^3+9090x^4+42828x^5+9090x^6+1848x^7+381x^8+34x^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 0.12 seconds.