The generator matrix

 1  0  1  1  1
 0  1  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+30x^1+333x^2+1960x^3+9138x^4+42612x^5+9138x^6+1960x^7+333x^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 0.123 seconds.