The generator matrix

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

generates a code of length 17 over GR(16,4) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+84x^39+363x^40+468x^41+240x^42+1008x^43+1140x^44+1392x^45+2160x^46+4536x^47+3465x^48+5112x^49+6480x^50+9072x^51+5070x^52+6768x^53+6480x^54+6804x^55+3093x^56+1620x^57+120x^60+54x^64+6x^68

The gray image is a code over GF(4) with n=68, k=8 and d=39.
This code was found by Heurico 1.16 in 3.45 seconds.