The generator matrix

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

generates a code of length 10 over GR(16,4) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+192x^21+1248x^22+1086x^24+1728x^25+3744x^26+3072x^27+6096x^28+5184x^29+13344x^30+9216x^31+9135x^32+5184x^33+6240x^34+48x^36+18x^40

The gray image is a code over GF(4) with n=40, k=8 and d=21.
This code was found by Heurico 1.16 in 1.12 seconds.