The generator matrix

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

generates a code of length 18 over GR(16,4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+144x^44+108x^45+84x^46+432x^47+1143x^48+456x^49+324x^50+624x^51+2553x^52+1152x^53+636x^54+1296x^55+3978x^56+1272x^57+492x^58+720x^59+846x^60+84x^61+30x^64+9x^68

The gray image is a code over GF(4) with n=72, k=7 and d=44.
This code was found by Heurico 1.16 in 0.203 seconds.