The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+94x^46+366x^47+1041x^48+1372x^49+1906x^50+2256x^51+2700x^52+2176x^53+1757x^54+1226x^55+817x^56+308x^57+165x^58+68x^59+70x^60+32x^61+21x^62+4x^63+3x^64+1x^66

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 2.4 seconds.