The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+132x^40+156x^41+144x^42+150x^44+528x^45+1296x^46+168x^48+2088x^49+3888x^50+186x^52+2832x^53+3888x^54+204x^56+540x^57+138x^60+39x^64+6x^68

The gray image is a code over GF(4) with n=68, k=7 and d=40.
This code was found by Heurico 1.16 in 0.271 seconds.