The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^46+148x^47+431x^48+522x^49+1187x^50+1008x^51+1542x^52+1004x^53+1151x^54+496x^55+411x^56+132x^57+47x^58+8x^59+9x^60+4x^61+9x^62+4x^63+1x^64+2x^65+2x^66+5x^68+2x^70

The gray image is a code over GF(2) with n=416, k=13 and d=184.
This code was found by Heurico 1.16 in 0.792 seconds.