The generator matrix

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

generates a code of length 16 over GR(16,4) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+96x^39+201x^40+792x^41+96x^42+864x^43+480x^44+1464x^45+576x^46+2592x^47+1053x^48+2376x^49+864x^50+2592x^51+768x^52+1512x^53+51x^56+6x^64

The gray image is a code over GF(4) with n=64, k=7 and d=39.
This code was found by Heurico 1.16 in 8.48 seconds.