The generator matrix

 1  1  1  1
 0  2  0  0
 0  0  2  0
 0  0  0  2

generates a code of length 4 over GR(16,4) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+12x^4+54x^8+876x^12+81x^16

The gray image is a code over GF(4) with n=16, k=5 and d=4.
This code was found by Heurico 1.16 in -3.62e-008 seconds.