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

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

Homogenous weight enumerator: w(x)=1x^0+131x^48+364x^49+839x^50+1416x^51+2279x^52+3252x^53+4869x^54+6636x^55+8207x^56+9352x^57+8434x^58+6812x^59+4981x^60+3304x^61+2043x^62+1188x^63+711x^64+364x^65+177x^66+76x^67+64x^68+4x^69+20x^70+10x^72+1x^74+1x^82

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 59 seconds.