The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+173x^44+312x^45+1067x^46+1176x^47+2141x^48+2076x^49+2661x^50+2228x^51+2023x^52+1024x^53+811x^54+304x^55+239x^56+44x^57+63x^58+4x^59+24x^60+6x^62+7x^64

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 2.42 seconds.