The generator matrix

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

generates a code of length 9 over GR(16,4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+42x^20+84x^24+768x^27+36x^28+75x^32+18x^36

The gray image is a code over GF(4) with n=36, k=5 and d=20.
This code was found by Heurico 1.16 in 1.01e-007 seconds.