The generator matrix

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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+82x^42+348x^43+811x^44+1896x^45+2842x^46+5062x^47+7233x^48+9586x^49+9935x^50+9622x^51+7147x^52+5220x^53+2751x^54+1616x^55+767x^56+346x^57+131x^58+82x^59+38x^60+8x^61+3x^62+6x^63+3x^64

The gray image is a code over GF(2) with n=400, k=16 and d=168.
This code was found by Heurico 1.16 in 34.3 seconds.