The generator matrix

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

generates a code of length 20 over GR(16,4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+144x^44+12x^45+462x^48+180x^49+192x^51+2382x^52+1080x^53+1728x^55+8049x^56+3240x^57+5184x^59+16536x^60+4860x^61+5184x^63+12462x^64+2916x^65+534x^68+303x^72+84x^76+3x^80

The gray image is a code over GF(4) with n=80, k=8 and d=44.
This code was found by Heurico 1.16 in 4.42 seconds.