The generator matrix

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

generates a code of length 17 over GR(16,4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+180x^41+60x^42+96x^43+507x^44+840x^45+540x^46+288x^47+672x^48+2016x^49+1620x^50+1440x^51+1341x^52+3096x^53+1620x^54+480x^55+768x^56+780x^57+21x^60+15x^64+3x^68

The gray image is a code over GF(4) with n=68, k=7 and d=41.
This code was found by Heurico 1.16 in 0.203 seconds.