The generator matrix

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

generates a code of length 17 over GR(16,4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+306x^40+408x^41+492x^42+852x^43+1743x^44+1812x^45+1608x^46+2820x^47+5853x^48+4596x^49+3936x^50+7164x^51+11985x^52+6780x^53+4152x^54+4524x^55+4128x^56+1764x^57+564x^58+21x^60+24x^64+3x^68

The gray image is a code over GF(4) with n=68, k=8 and d=40.
This code was found by Heurico 1.16 in 2.97 seconds.