The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+170x^46+826x^47+1810x^48+3036x^49+3332x^50+4776x^51+4981x^52+4988x^53+3310x^54+2846x^55+1545x^56+648x^57+285x^58+106x^59+39x^60+48x^61+14x^62+4x^63+1x^66+2x^67

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 8.53 seconds.