The generator matrix

 1  1  1  1
 0  2  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+16x^1+108x^2+432x^3+2982x^4+432x^5+108x^6+16x^7+1x^8

The gray image is a code over GF(2) with n=32, k=12 and d=4.
This code was found by Heurico 1.16 in 0.000871 seconds.