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

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

Homogenous weight enumerator: w(x)=1x^0+116x^51+316x^52+494x^53+679x^54+916x^55+1048x^56+1326x^57+1018x^58+844x^59+606x^60+278x^61+179x^62+180x^63+75x^64+42x^65+32x^66+24x^67+9x^68+4x^69+4x^70+1x^84

The gray image is a code over GF(2) with n=456, k=13 and d=204.
This code was found by Heurico 1.16 in 0.999 seconds.