The generator matrix

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

generates a code of length 19 over GR(16,4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+54x^44+156x^48+174x^52+177x^56+3072x^57+177x^60+141x^64+120x^68+21x^72+3x^76

The gray image is a code over GF(4) with n=76, k=6 and d=44.
This code was found by Heurico 1.16 in 0.0382 seconds.