The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  0  1  1  6  1  1  1  1 12 10  1  1  0  1  1  6  1  1  1 12  1 10  1  0  1  6  1  1 10  1  1 10  1  6 12  1  0  1  1  1  1  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  1  0  5  1  6  3 12 15  1  1 10  9  1  0  5  1  3  9  6  1 15  1 10  1  3  1  5  6  1 15  6  1 10  1  1  9  1  3 10 10  6  5  3  6  6
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  8  8  8  0  8  0  8  8  8  0  0  8  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  8  0  8  8  0  8  8  8  0  8  0  0  8  0  8  8  8  0  8  0  0  8  0  8  8  8  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  8  0  0  8  0  0  8  0  0  8  0  0  0  8  8  0  8  0  0  8  8  8  0  8  8  0  0  0  0  8  0  8  0  0  0  8  8
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  8  8  0  0  8  0  8  8  8  0  0  0  0  8  8  0  8  8  0  0  8  0  8  8  0  8  8  8  0  8  8  8  8  0  8  0  8  8  8  8
 0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  0  8  0  8  8  8  0  0  8  0  8  8  8  8  8  0  0  8  8  8  0  8  8  0  8  0  0  8  0  0  8  0  8  0  0  0  8  0  8  8  8
 0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  0  8  8  8  0  0  8  0  0  0  8  8  0  0  0  8  8  8  8  0  0  8  8  0  0  0  8  0  8  8  8  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  8  8  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  0  8  8  8  0  8  8  0  8  8  8  8  0  8  8  0  0  0  0  8  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+114x^48+48x^49+142x^50+320x^51+765x^52+1344x^53+2216x^54+4032x^55+4499x^56+5920x^57+4388x^58+4032x^59+2295x^60+1344x^61+648x^62+320x^63+196x^64+48x^65+30x^66+35x^68+21x^72+9x^76+1x^80

The gray image is a code over GF(2) with n=456, k=15 and d=192.
This code was found by Heurico 1.16 in 12.2 seconds.