The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+135x^46+404x^47+853x^48+1284x^49+2124x^50+2164x^51+2700x^52+2268x^53+1932x^54+1132x^55+675x^56+332x^57+210x^58+76x^59+45x^60+20x^61+13x^62+11x^64+2x^66+3x^68

The gray image is a code over GF(2) with n=416, k=14 and d=184.
This code was found by Heurico 1.16 in 2.54 seconds.