The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  2  0  2  1  1  1  1 12  1  1  1  2  1  1  0  1  1  2  0  2  1  2  1  1  2  1 12  2  1  4  4  4  8  2  1
 0  2  0  6  4  6 12  2  6 14  8 12  0  2  4 10 14  0  4 14 14  2 14  2  6  4  6  4  4  2 10  8  6  2  0 10  2  6 12  6  2 14  6  2  8 10  2 14  2 14  2  4  8  8  0  0  0
 0  0 12  0  4  0  0  8  4 12  0  4  4 12  8  4  0  8  4  0  4 12  8  8  4 12 12  0 12  0  0  8 12  0  4  4  4  0  4  0  8  4  8  0 12 12  8  8  8  8  0  0  4 12  4  0  0
 0  0  0 12  0  0  0 12  4  8 12 12  4  8 12  4  4  8  0  8  8  0 12  0  4  8  4  8 12  8  0 12  4 12  0  8 12  0  0  0  0  8  4  4  4 12  4  4  0  0 12 12  4  8 12 12  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  0  0  8  8  8  8  8  0  0  8  8  8  0  0  0  8  0  8  8  0  8  8  8  8  0  8  8  8  8  0  0  0  8  0  0  8  8  0  8  0  8  0  0
 0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  0  8  8  8  8  8  8  0  8  8  0  8  0  0  8  0  0  0  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  0  8  8  0  0  8  8  0  8  0  8  0  0  8  8  0  8  0  0  8  8  8  8  0  0  0  0  8  0  0  8  0  8  8  8  0  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+41x^48+98x^49+184x^50+398x^51+571x^52+936x^53+1274x^54+1686x^55+2048x^56+2050x^57+2176x^58+1636x^59+1121x^60+874x^61+487x^62+352x^63+152x^64+124x^65+83x^66+22x^67+32x^68+14x^69+19x^70+2x^71+1x^72+1x^74+1x^80

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 5.05 seconds.