The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  0  1  1  1  6  1  1 10  1  1 12  1  1  0  1  1  6  1  1 12  1 10  1  1  1 10  1 10  0  0  1 12  1  2 12  1  1  1  1  1  6 12  2  0
 0  1  3  6  5  1 12 15  1 10  9  1  0  1  3  6  5  1 12  9  1 10 15  1  0  9  1  6  3  1 15 12  1 10  1  3  5  0  1 15  1  1  1  6  1 12 12  1 10  5  0 12 15  1  1  0  1
 0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  0  8  8  8  8  8  0  8  0  0  0  8  8  8  8  0  8  8  8  8  8  0  8  0  8  8  8  0  8  0  8  0  8  0  8  0  0  8  0  8  0  0
 0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0  0  0  0  0  8  8  8  8  8  8  0  0  0  0  8  8  0  0  8  0  8  0  8  8  8  8  8  0  0  8  0  8  0  8  0  0  8  0
 0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  8  0  8  0  8  8  8  0  0  0  8  0  0  8  0  8  0  0  8  0  0  8  8  8  8  0  0  8  8  0  0  8  0  0  0  8  8  0  0
 0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  0  8  0  8  0  8  8  8  0  0  0  8  8  0  8  0  8  0  8  0  0  8  0  8  8  0  8  8  0  0  0  0  0  8  8  8  8  0  0  0  8
 0  0  0  0  0  0  8  8  0  8  0  8  8  8  8  8  8  8  8  0  0  8  0  0  0  0  8  0  8  0  0  0  8  8  0  8  8  0  0  0  8  0  8  8  0  0  8  0  8  0  8  8  8  8  0  8  8

generates a code of length 57 over Z16 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+19x^50+112x^51+190x^52+436x^53+542x^54+1060x^55+1056x^56+1424x^57+1052x^58+1016x^59+526x^60+436x^61+163x^62+116x^63+13x^64+8x^65+7x^66+4x^68+4x^70+2x^72+2x^74+3x^78

The gray image is a code over GF(2) with n=456, k=13 and d=200.
This code was found by Heurico 1.16 in 0.801 seconds.