The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+232x^46+744x^47+1694x^48+3040x^49+3428x^50+5100x^51+4683x^52+4856x^53+3602x^54+2836x^55+1362x^56+656x^57+274x^58+148x^59+52x^60+24x^61+14x^62+4x^63+15x^64+2x^66+1x^68

The gray image is a code over GF(2) with n=416, k=15 and d=184.
This code was found by Heurico 1.16 in 7.7 seconds.