The generator matrix

 1  0  1  1  1  4  1 10  1  1  6  1  1  4  1  4  1  1  1  1  1  2 10  1  2  1  1  1 12  1 10 12  1  1  1  1  1  0 14  1  2  8  1  1  1  0  1  2  1 12  0  1  8 14  2  0  1
 0  1  1  0 11  1 10  1  5  6  1  7 15  1 12  1 10  1  7  1 14  1  1  7  1  6  9 14  1 12  1  1  9  3  7  6  8  2  1 14 10 12 12  5 15  1 13 12  9  2  1 11  2  1  2  2  0
 0  0  2  6  4  6 10 10  0  0  8  2  2 10  6  0  4  6  0  8 14  6  6  6  8 14  2  0  8  0 12  4  8 14 12  6  4  2 14  6 10  2  8 12  6  0  4  6  2  6  6  2 10  4 12  4  0
 0  0  0 12  0  4 12  4  0  0  0  8  4  0  0  4 12 12  4  4 12  4  8 12  4  8 12 12  8  0 12  4  0  0  0  0  8 12  4 12  8  8  4  0 12  8  4  4 12  4  8  0  8 12 12  4  0
 0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  8  0  8  0  8  8  0  8  8  0  0  0  8  0  8  8  8  8  8  0  8  8  0  8  8  8  8  0  0
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  0  8  8  8  8  8  8  8  0  0  0  8  0  8  0  8  0  8  0  0  8  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  8  8  8  8  8  8  0  0  0  8  8  8  8  0  8  8  8  8  8  8  0  0  8  8  8  8  8  8  8  0  0  0  0  8  0  8  8  0  0  0  8  8  8  8  0  8  8  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+89x^48+246x^49+419x^50+1160x^51+1767x^52+3508x^53+5120x^54+7138x^55+8389x^56+9628x^57+8651x^58+7460x^59+5267x^60+3242x^61+1439x^62+1076x^63+441x^64+252x^65+100x^66+60x^67+40x^68+18x^69+13x^70+2x^71+4x^72+2x^73+2x^74+2x^76

The gray image is a code over GF(2) with n=456, k=16 and d=192.
This code was found by Heurico 1.16 in 41.7 seconds.