The generator matrix

 1  1  1  1  1
 0  2  0  0  8
 0  0  2  0  0
 0  0  0  2  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+22x^1+205x^2+1096x^3+3634x^4+22852x^5+3634x^6+1096x^7+205x^8+22x^9+1x^10

The gray image is a code over GF(2) with n=40, k=15 and d=4.
This code was found by Heurico 1.16 in 0.0466 seconds.