The generator matrix

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

generates a code of length 10 over GR(16,4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+78x^24+324x^25+144x^26+144x^27+459x^28+648x^29+288x^30+432x^31+666x^32+756x^33+144x^34+9x^36+3x^40

The gray image is a code over GF(4) with n=40, k=6 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.