The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12  2  1  2  2  4  2  0  1  1  8  0  8 12  8  4  2  1  1  1  1  0  1  1 12  2  1
 0  2  0  0  0  2  6 14 12 10 12  6 14  4  8  2  2  2  0  0  8 14  8  2 12  6 14  8  2 12  2 12  4 12 12  0  0  2  2  2  0 12  4 10  2  6 12  2  4  0
 0  0  2  0  2  2  2  0  8  2 10  4 12  0  6 14  6  4 12  2 14  8 12 12  2 10 14  2  4 12 14 12  2  2  2  4  2  0 14  2 12  6  0  0  6  6 10  6  2  0
 0  0  0  2  2  0  2  2 14  4  2 10  0 12 12  6 12  6 12 12  2  4  2  2 12  6  4  6  0 10 14  4 12  8  2  2  6 12  8 14  8  6  0  4 10  8 14 14  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  0  8  8  8  0  0  8  0  8  8  8  0  8  0  0  0  0  8  8  0  8  8  8  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  0  0  8  8  0  0  0  0  0  8  8  8  0  8  0  8  8  8  0  8  8  0  0
 0  0  0  0  0  0  8  8  8  0  8  0  8  8  8  0  8  8  0  8  8  0  0  8  0  0  8  8  8  8  8  0  8  8  0  0  0  0  0  8  8  8  0  0  0  8  8  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+46x^41+326x^42+566x^43+1015x^44+2174x^45+2830x^46+5374x^47+5999x^48+9788x^49+9126x^50+9796x^51+6475x^52+5404x^53+2674x^54+2040x^55+902x^56+490x^57+264x^58+142x^59+69x^60+14x^61+8x^62+2x^63+2x^64+4x^65+4x^66+1x^68

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 48.4 seconds.