The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+315x^24+1500x^28+2205x^32+60x^36+15x^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 0.00715 seconds.