The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^51+211x^52+492x^53+638x^54+1012x^55+1070x^56+1246x^57+1154x^58+1040x^59+537x^60+420x^61+185x^62+62x^63+27x^64+14x^65+2x^66+2x^67+7x^68+4x^69+4x^70+2x^71+2x^72+1x^76+1x^78

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 0.863 seconds.