The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+158x^44+276x^45+990x^46+1452x^47+2763x^48+3584x^49+4605x^50+5232x^51+4641x^52+3708x^53+2585x^54+1324x^55+877x^56+232x^57+185x^58+56x^59+57x^60+8x^61+17x^62+15x^64+2x^66

The gray image is a code over GF(2) with n=408, k=15 and d=176.
This code was found by Heurico 1.16 in 9.76 seconds.