The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+36x^41+381x^42+796x^43+1586x^44+2724x^45+4917x^46+7280x^47+10104x^48+10064x^49+9961x^50+7388x^51+4899x^52+2700x^53+1495x^54+604x^55+357x^56+116x^57+74x^58+24x^59+11x^60+8x^61+4x^62+4x^63+2x^64

The gray image is a code over GF(2) with n=392, k=16 and d=164.
This code was found by Heurico 1.16 in 33.6 seconds.