The generator matrix

 1  1  1
 0 12  8
 0  0  4

generates a code of length 3 over Z16 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+6x^1+15x^2+212x^3+15x^4+6x^5+1x^6

The gray image is a code over GF(2) with n=24, k=8 and d=4.
This code was found by Heurico 1.16 in 0.0108 seconds.