The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+24x^46+70x^47+76x^48+192x^49+283x^50+366x^51+772x^52+520x^53+789x^54+402x^55+271x^56+176x^57+48x^58+58x^59+26x^60+8x^61+2x^62+3x^64+5x^66+2x^68+1x^72+1x^86

The gray image is a code over GF(2) with n=424, k=12 and d=184.
This code was found by Heurico 1.16 in 0.372 seconds.