The generator matrix

 1  0  0  0  1  1  1  1  1  1  2  1 2a+2  1  1  2  1  1
 0  1  0  0  0  2  2 2a+3  1  a  1  1  1 a+1 3a+1  1  1  2
 0  0  1  0  1 3a+2 a+1  a 3a+3  1 2a+1  0 a+2 a+2  a 3a+2 a+1 2a+2
 0  0  0  1 3a+3  a  1  0  a  1 a+1  3 a+1 2a a+3 2a+3  3 2a+2
 0  0  0  0  2  0 2a 2a+2  2 2a+2  0 2a  2  2  0 2a+2 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+201x^40+216x^41+192x^42+1068x^43+2841x^44+1776x^45+1812x^46+4848x^47+10806x^48+8304x^49+6960x^50+17832x^51+32637x^52+21024x^53+17016x^54+30000x^55+43740x^56+21624x^57+10608x^58+13836x^59+12003x^60+2352x^61+276x^62+129x^64+39x^68+3x^72

The gray image is a code over GF(4) with n=72, k=9 and d=40.
This code was found by Heurico 1.16 in 44.7 seconds.