The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+338x^51+961x^52+1778x^53+2962x^54+3538x^55+4573x^56+4678x^57+4729x^58+3506x^59+2646x^60+1630x^61+849x^62+306x^63+113x^64+74x^65+35x^66+20x^67+25x^68+1x^70+4x^71+1x^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 49.2 seconds.