The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+356x^51+834x^52+2184x^53+2450x^54+3918x^55+4033x^56+5352x^57+4090x^58+4100x^59+2373x^60+1758x^61+672x^62+362x^63+116x^64+100x^65+18x^66+28x^67+1x^68+14x^69+2x^70+4x^71+2x^72

The gray image is a code over GF(2) with n=456, k=15 and d=204.
This code was found by Heurico 1.16 in 74.7 seconds.