The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+57x^48+80x^50+112x^51+316x^52+384x^53+478x^54+1040x^55+893x^56+1536x^57+838x^58+1040x^59+513x^60+384x^61+250x^62+112x^63+104x^64+18x^66+17x^68+9x^72+9x^76+1x^84

The gray image is a code over GF(2) with n=456, k=13 and d=192.
This code was found by Heurico 1.16 in 1.27 seconds.