The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  4  1  4  2  1  2  2  1  1  1  4  4  8  1  1  1  1  2  1  4  2
 0 12  0  0  0  0  0  0  0  0  8  4 12 12  8  0 12 12  4 12  4  0 12  4  4  4  8  4 12  4  8  8 12  4  4  8  0  4  4  0  0  4 12  0 12  4  0  8  4  8 12  4  8 12  0  0  4
 0  0 12  0  0  0  0  0  0  0 12  8  4 12  4  4  4  0  4  8  8 12  4  0 12  4  4  8  4  0  4  8 12  0  4  0  4  8  4  8 12 12  0 12  0  0 12  0  8  4 12  4 12 12  8  4  4
 0  0  0 12  0  0  8 12 12  4  4 12  8 12 12  0  8  8  0 12 12  4  4  4  8  4 12  0 12  0  8  0  4  8  8  0  8  8 12  4  0  0  4  4  4 12  0  8 12  8 12  4 12  8  0 12  0
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  8  0 12  4  4  4  0  4  4 12  8  4  4  4  8  0  4  0  8  0  4  4  8  4  0  8 12 12  4 12 12  8  4  4 12 12  4  4  8 12  8  0  8
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  4  4  0 12  4  8  4  8  0  4 12  4 12  0  4  4 12  8  8 12  4  8 12  8  4  0  0 12  8 12  4 12  4 12  4 12  4 12 12  0  4  0  0

generates a code of length 57 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+194x^48+4x^49+402x^50+40x^51+628x^52+336x^53+1226x^54+1480x^55+2732x^56+2392x^57+2732x^58+1528x^59+1193x^60+336x^61+518x^62+24x^63+310x^64+4x^65+174x^66+91x^68+36x^70+2x^72+1x^88

The gray image is a code over GF(2) with n=456, k=14 and d=192.
This code was found by Heurico 1.16 in 6.54 seconds.