The generator matrix

 1  0  1  1  1  1  1  1  1  2
 0  1 2a+3  a a+1  2 2a+1 a+2 a+3  1

generates a code of length 10 over GR(16,4) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+120x^28+135x^32

The gray image is a code over GF(4) with n=40, k=4 and d=28.
This code was found by Heurico 1.16 in 1.01e-007 seconds.