The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  0  1  1  1  1  1  1  1  1  1
 0  1  1  a 3a+3  0 2a+3  a a+1  1  0  1 2a+3  a a+1  a 2a+3 a+1 2a+3  0  0
 0  0 2a+2  0  0  0  0  2  2  2 2a 2a  0  2  0  2  2  2  2  0  0
 0  0  0  2  0  0  2 2a+2 2a+2  0 2a+2 2a 2a 2a+2 2a+2  2  0  2 2a  0  0
 0  0  0  0 2a+2  0 2a  0 2a 2a 2a 2a 2a 2a 2a+2  2 2a 2a+2  2 2a  0
 0  0  0  0  0  2 2a  2  0 2a+2 2a+2 2a  2 2a+2  0 2a  2 2a 2a+2 2a  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+57x^44+300x^48+96x^51+1008x^52+192x^54+1152x^55+2964x^56+1728x^58+5184x^59+6426x^60+5184x^62+10368x^63+9447x^64+5184x^66+7776x^67+7632x^68+540x^72+213x^76+60x^80+24x^84

The gray image is a code over GF(4) with n=84, k=8 and d=44.
This code was found by Heurico 1.16 in 4.4 seconds.