The generator matrix

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

generates a code of length 16 over GR(16,4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+369x^44+279x^48+372x^52+3x^60

The gray image is a code over GF(4) with n=64, k=5 and d=44.
This code was found by Heurico 1.16 in 0 seconds.