The generator matrix

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

generates a code of length 10 over GR(16,4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+90x^20+180x^24+180x^28+3072x^30+315x^32+210x^36+48x^40

The gray image is a code over GF(4) with n=40, k=6 and d=20.
This code was found by Heurico 1.16 in 0.0109 seconds.