The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+132x^49+466x^50+1064x^51+1979x^52+3010x^53+5221x^54+7082x^55+8954x^56+9584x^57+9260x^58+7348x^59+5038x^60+2978x^61+1727x^62+802x^63+488x^64+202x^65+116x^66+32x^67+17x^68+12x^69+10x^70+8x^71+3x^72+2x^73

The gray image is a code over GF(2) with n=456, k=16 and d=196.
This code was found by Heurico 1.16 in 40.9 seconds.