The generator matrix

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

generates a code of length 4 over Z16 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+40x^1+636x^2+5272x^3+20870x^4+5272x^5+636x^6+40x^7+1x^8

The gray image is a code over GF(2) with n=32, k=15 and d=4.
This code was found by Heurico 1.16 in 0.078 seconds.