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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+68x^46+134x^47+221x^48+290x^49+358x^50+490x^51+831x^52+1624x^53+2188x^54+3314x^55+4591x^56+4590x^57+4332x^58+3590x^59+2418x^60+1422x^61+772x^62+548x^63+310x^64+212x^65+180x^66+104x^67+71x^68+50x^69+36x^70+12x^71+5x^72+4x^73+1x^74+1x^90

The gray image is a code over GF(2) with n=456, k=15 and d=184.
This code was found by Heurico 1.16 in 23.2 seconds.