The generator matrix

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

generates a code of length 16 over GR(16,4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+252x^35+324x^36+852x^37+1248x^38+2160x^39+3015x^40+4272x^41+4224x^42+12648x^43+13125x^44+15864x^45+16704x^46+34128x^47+29214x^48+28848x^49+22656x^50+34428x^51+19662x^52+11604x^53+4320x^54+2400x^55+123x^56+57x^60+15x^64

The gray image is a code over GF(4) with n=64, k=9 and d=35.
This code was found by Heurico 1.16 in 37.2 seconds.