The generator matrix

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

generates a code of length 21 over GR(16,4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+51x^44+243x^48+402x^52+192x^54+480x^56+1728x^58+513x^60+5184x^62+759x^64+5184x^66+801x^68+540x^72+228x^76+57x^80+21x^84

The gray image is a code over GF(4) with n=84, k=7 and d=44.
This code was found by Heurico 1.16 in 0.58 seconds.