The generator matrix

 1  0  1  1  1  6  1 10  1  1 12  1  1  1 14  8  1  1  1 14  1  2  1  1  1  1  2  1  1  1  1  1  1  1  1  0  1  1  1  2 12  1  8  2  1  1  2  1  1  8 14  1
 0  1 11  6 13  1  2  1 11 12  1 13  8  3  1  1  5  6 11  1  0  1  1 10 15  0  1  6 15  1 12 15  5  3  6  1  5  5  8  4  2  2  4  1 12  5  1  5 12  1  1  3
 0  0 12  0  4  4  8  4  0  8  0  0  4  4  0  0  0  4  8 12 12  8 12  8  8  8  4  4 12 12  0  0 12  0  4 12  0 12  8 12  8  8 12  8  4  4 12 12  8  8  0  0
 0  0  0 12  0  4  4 12  4  0  0  4  8  4  4 12  8 12  8  8 12 12  8  0  8 12  8  8  4  4  8  0  0 12 12 12  0 12  4  0 12  0  4  8  0  4 12  0 12  4  8  0
 0  0  0  0  8  0  8  8  0  8  8  8  8  8  0  8  0  8  8  8  0  0  0  0  0  8  0  0  0  8  8  8  8  8  0  0  0  8  0  8  0  8  0  0  0  8  8  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+33x^46+220x^47+410x^48+838x^49+846x^50+1292x^51+1016x^52+1260x^53+912x^54+756x^55+288x^56+194x^57+49x^58+30x^59+8x^60+8x^61+10x^62+4x^63+5x^64+4x^65+5x^66+2x^67+1x^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 0.732 seconds.