The generator matrix

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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+93x^44+346x^45+913x^46+1248x^47+2130x^48+2248x^49+2706x^50+2164x^51+2015x^52+1218x^53+765x^54+218x^55+152x^56+92x^57+36x^58+16x^59+15x^60+4x^62+2x^63+1x^64+1x^68

The gray image is a code over GF(2) with n=400, k=14 and d=176.
This code was found by Heurico 1.16 in 2.37 seconds.