The generator matrix

 1  0  1  1  1 12  1  1  2  1  1  6 10  1  1  1  1 12  1  1  1  1  1  8  1 14  1  8  8 10  1  0  1  1  2 10 12  4  1  1  1  1  1 10  1  1  8  6  1  1
 0  1  1 12 11  1  2  7  1  5 14  1  1  8  9  2  7  1  1  8 13  0  6  1 11  1 15  1  1  1 15  1  7  6  4  1  2  4  6  0  8 10  2  1  7  1  0  1  3  0
 0  0  2  6  4  6  2 14 10  0  4  0 14  4  0  4  2  0 12  2  2  6  0  2 10  4  8 10  4  8  6  6 12  6  2  0  6  2  8  8 10  6  4  0 12 12  2  6 14  0
 0  0  0  8  0  0  0  0  8  8  0  0  0  0  8  0  8  8  0  8  8  0  0  0  8  0  8  0  0  0  0  8  0  0  8  8  8  0  0  8  8  8  8  0  8  8  0  8  8  8
 0  0  0  0  8  0  0  0  0  8  0  8  0  8  8  8  8  0  0  8  0  8  8  0  0  0  0  8  0  8  0  8  0  8  0  8  8  0  8  0  0  8  8  0  8  0  0  0  8  8
 0  0  0  0  0  8  0  0  8  0  0  8  8  8  0  8  8  0  8  8  0  8  8  0  0  8  8  8  8  0  8  0  0  0  8  8  8  0  0  0  8  0  0  0  0  0  0  8  8  8
 0  0  0  0  0  0  8  0  8  8  0  8  0  8  8  8  0  8  8  0  8  8  0  8  0  0  8  0  8  8  8  8  8  0  0  8  8  0  8  8  8  0  8  8  0  0  0  0  8  8
 0  0  0  0  0  0  0  8  0  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  8  8  8  0  0  0  8  8  0  0  0  8  8  8  8  8  0  8  8  0  0  0  0  0  0  8

generates a code of length 50 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+28x^41+146x^42+342x^43+827x^44+1304x^45+3089x^46+3808x^47+9047x^48+7264x^49+13617x^50+7376x^51+9329x^52+3904x^53+2974x^54+1228x^55+708x^56+276x^57+123x^58+42x^59+51x^60+24x^61+15x^62+4x^63+4x^64+1x^66+1x^68+2x^70+1x^74

The gray image is a code over GF(2) with n=400, k=16 and d=164.
This code was found by Heurico 1.16 in 34.2 seconds.