The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1236x^44+1440x^46+4818x^48+4320x^50+12312x^52+11616x^54+17466x^56+7200x^58+5076x^60+45x^64+6x^72

The gray image is a code over GF(4) with n=72, k=8 and d=44.
This code was found by Heurico 1.16 in 63.4 seconds.