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

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

Homogenous weight enumerator: w(x)=1x^0+60x^51+189x^52+186x^53+335x^54+364x^55+657x^56+578x^57+649x^58+410x^59+287x^60+112x^61+120x^62+56x^63+42x^64+18x^65+14x^66+6x^67+8x^68+2x^69+1x^70+1x^90

The gray image is a code over GF(2) with n=456, k=12 and d=204.
This code was found by Heurico 1.16 in 0.568 seconds.