The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+119x^46+258x^47+400x^48+402x^49+729x^50+436x^51+752x^52+332x^53+254x^54+146x^55+113x^56+74x^57+48x^58+8x^59+14x^60+8x^61+1x^62+1x^74

The gray image is a code over GF(2) with n=408, k=12 and d=184.
This code was found by Heurico 1.16 in 0.384 seconds.