The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+561x^44+456x^45+1080x^46+1680x^47+2925x^48+3744x^49+6144x^50+4368x^51+10050x^52+15360x^53+18864x^54+13680x^55+23139x^56+36720x^57+31680x^58+17328x^59+23886x^60+22968x^61+15960x^62+5952x^63+4890x^64+624x^65+42x^68+21x^72+21x^76

The gray image is a code over GF(4) with n=76, k=9 and d=44.
This code was found by Heurico 1.16 in 44.9 seconds.