The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+9x^24+27x^28+192x^30+12x^32+9x^36+6x^40

The gray image is a code over GF(4) with n=40, k=4 and d=24.
This code was found by Heurico 1.16 in 0 seconds.