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

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

Homogenous weight enumerator: w(x)=1x^0+180x^51+234x^52+620x^53+599x^54+940x^55+987x^56+1242x^57+996x^58+962x^59+511x^60+388x^61+196x^62+180x^63+47x^64+50x^65+38x^67+7x^68+4x^69+1x^70+4x^71+4x^72+1x^80

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 1.51 seconds.