The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^51+131x^52+256x^53+249x^54+598x^55+389x^56+808x^57+431x^58+568x^59+209x^60+198x^61+82x^62+52x^63+31x^64+12x^65+3x^66+6x^67+6x^68+6x^69+2x^70+2x^71+1x^72+2x^75+1x^86

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 0.466 seconds.