The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  2  0 2a 2a  2 2a+2 2a+2  2 2a  2 2a  2
 0  0  2  0  0 2a+2  2  0 2a 2a 2a  2 2a  0 2a+2  0 2a+2
 0  0  0  2  0  2 2a+2 2a+2 2a  0 2a  2  0  2 2a+2  2  0
 0  0  0  0  2 2a+2 2a  2 2a+2  2  0  2 2a  2 2a 2a  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+150x^44+168x^48+3072x^51+186x^52+204x^56+138x^60+39x^64+6x^68

The gray image is a code over GF(4) with n=68, k=6 and d=40.
This code was found by Heurico 1.16 in 0.0338 seconds.