The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  1  1  1  1  1  1  1  1  0  1  1  2  2  1  1  2  1  1  1  0  1  2  2 12  1  1 12  1  4  1  2  1
 0  2  0  6  4  6 12  2  8  6  0 14  4  2  4 10  6  2  0 10 12  2 14  4  6 12 12 14  2  6  6 14 14  0 12 12  2  6  2  2  2 10 10  2  4  2  2 14  2 12  8  0
 0  0 12  0  4  0  0  8  0  4  4 12  8 12  4 12  8  0  8  0  0 12  4  8 12  0 12 12  8  8  4  8 12  4  8 12  8  8 12  4  4 12 12  0  4  8  4 12  8 12  0  4
 0  0  0 12  0  0  8  4  4  4  4  8 12  0  4  4  0 12  8  8  8  8  4 12 12  4  4  0  8  4  0  4  0  8  8 12  8 12  4 12  8  4 12  0 12  4  4  4 12  0 12 12
 0  0  0  0  8  8  8  8  0  0  0  8  8  0  8  8  8  8  8  8  0  0  8  0  0  8  0  0  0  8  8  0  8  8  8  0  8  0  0  0  8  8  0  8  0  0  0  8  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+40x^46+116x^47+222x^48+330x^49+324x^50+870x^51+426x^52+832x^53+274x^54+296x^55+164x^56+78x^57+60x^58+22x^59+12x^60+4x^61+5x^62+8x^63+5x^64+4x^65+2x^68+1x^78

The gray image is a code over GF(2) with n=416, k=12 and d=184.
This code was found by Heurico 1.16 in 0.387 seconds.