The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  4  2  1  1  1  1  2  8  1  2 12 12  2  2  2  1 12  2  1  1  2  1  2  4  8  0  1  2  1  1
 0  2  0  0  0  2 14  2  4  2 12  2 10  8  2  4 14  4 14  0 12 12 12 10 10  8  2  2 12  4  2  2 10 12  0 12  2  0  2  0  8  6  2  8  2  0  6  2  0  0
 0  0  2  0  2  2  2  8 14  6  8  0 14 12 12 10  6  2  0  2  4 10  0 12 14  2 14 12  0  0 14  4  6 14  0  6  6  4  6 12  6  2  4  2 14  8  0 14  4  0
 0  0  0  2  2  0 10  2  0  8  8  8 10 14 14  2  4  8 12  2  2 12  6 10  6  2  4 12  4  6 10 14  6 10  2  0  4 14  4  4 14  0 10  2 10  2  2 10  0  4
 0  0  0  0  4  0  4  0 12 12 12  4  8  4 12  0  0  8  8 12 12 12  0  0  8  0  0 12  8 12  4  4  0  8  8 12 12  0 12  8  4  4  4  4  8  4  0  0  0  4
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  8  8  0  8  8  8  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+80x^41+263x^42+652x^43+1150x^44+1940x^45+3462x^46+4302x^47+7649x^48+8414x^49+9775x^50+8162x^51+7832x^52+4726x^53+3281x^54+1770x^55+1028x^56+522x^57+291x^58+114x^59+62x^60+30x^61+12x^62+8x^63+6x^64+3x^66+1x^70

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 49.3 seconds.