The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+192x^40+96x^42+492x^44+576x^46+1065x^48+864x^50+756x^52+30x^56+24x^60

The gray image is a code over GF(4) with n=64, k=6 and d=40.
This code was found by Heurico 1.16 in 0.0186 seconds.