The generator matrix

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

generates a code of length 15 over GR(16,4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+180x^40+405x^44+435x^48+3x^60

The gray image is a code over GF(4) with n=60, k=5 and d=40.
This code was found by Heurico 1.16 in -3.62e-008 seconds.