The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  0  0  1  1  1  1  1
 0  1  1  a 3a+3  0 2a+3  a a+1  1 2a+3 a+1  1  1  0  a  0 2a+3  2
 0  0 2a+2  0  0  2  0 2a 2a 2a+2 2a+2 2a 2a  0 2a+2 2a+2 2a+2 2a 2a+2
 0  0  0  2  0 2a+2 2a 2a+2  0 2a+2 2a+2 2a+2 2a 2a+2  2  0  0 2a  0
 0  0  0  0 2a+2  2  2 2a+2 2a 2a  2  0 2a 2a+2 2a  2 2a+2  0  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+54x^44+12x^45+60x^46+258x^48+336x^49+240x^50+1032x^52+1224x^53+840x^54+2745x^56+2640x^57+1200x^58+2805x^60+1932x^61+732x^62+147x^64+90x^68+33x^72+3x^76

The gray image is a code over GF(4) with n=76, k=7 and d=44.
This code was found by Heurico 1.16 in 0.286 seconds.