The generator matrix

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

generates a code of length 18 over GR(16,4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+33x^40+36x^41+36x^42+156x^43+867x^44+576x^45+432x^46+816x^47+2136x^48+3960x^49+1944x^50+2376x^51+5982x^52+11376x^53+3888x^54+3696x^55+7335x^56+11268x^57+2916x^58+2172x^59+2967x^60+432x^61+105x^64+24x^68+6x^72

The gray image is a code over GF(4) with n=72, k=8 and d=40.
This code was found by Heurico 1.16 in 3.38 seconds.