The generator matrix

 1  0  1  1
 0  1  0  8
 0  0  2  0
 0  0  0  4

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

Homogenous weight enumerator: w(x)=1x^0+24x^1+188x^2+1064x^3+5638x^4+1064x^5+188x^6+24x^7+1x^8

The gray image is a code over GF(2) with n=32, k=13 and d=4.
This code was found by Heurico 1.16 in 0.00201 seconds.