The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+30x^41+94x^42+138x^43+395x^44+544x^45+1560x^46+2578x^47+4579x^48+8128x^49+8712x^50+11986x^51+8788x^52+8162x^53+4641x^54+2570x^55+1478x^56+488x^57+314x^58+124x^59+107x^60+54x^61+30x^62+12x^63+6x^64+2x^65+8x^66+6x^68+1x^70

The gray image is a code over GF(2) with n=408, k=16 and d=164.
This code was found by Heurico 1.16 in 37.3 seconds.