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  2  1  1  1  1  1  1  1  2  2  1  1  1  1  2  2  1  1  1  2  2  1  1  2  0  1  2  1  1  2  1  1  1
 0 12  0  0  0  0  0  0  0  4 12 12  4 12  4 12  8 12  8 12  0  8  8  4  4  4  0  4  0  8  8  4  4 12  4  4  4  4  4 12  4 12  8  0  4  0  4  8  8  8  4  8  0  8 12  4  4
 0  0 12  0  0  8 12 12  4  4  4  8  4 12  0  8  0  8  0  4  4  4  8 12  8  0  4 12  4  0  0  0  0  0  0  4 12  8 12  4  4  0  8  4  8 12  8  8  4  0  4 12  0  4  8  0 12
 0  0  0 12  0 12 12  4  8  0  0  0  4 12  4  4  8 12  4  4  8  8  8  0  8 12 12  0 12  8  0  0  4  0  8 12  0  4  8 12 12  4  4  4  0 12  8  4 12 12  8 12  8 12  8  8  0
 0  0  0  0 12  4  8  4  4  0  4  4  4  0  8 12 12  8  8  4  8 12  4  4 12  4  4  0  0  0  0  4  0  8  4  0 12  0  8 12  8 12  8  0  8 12  4  0 12  0 12  8  8 12  0 12  8

generates a code of length 57 over Z16 who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+42x^50+84x^51+96x^52+174x^53+165x^54+182x^55+762x^56+1232x^57+723x^58+174x^59+119x^60+104x^61+65x^62+36x^63+33x^64+32x^65+24x^66+18x^67+11x^68+10x^69+4x^70+2x^71+2x^72+1x^90

The gray image is a code over GF(2) with n=456, k=12 and d=200.
This code was found by Heurico 1.16 in 0.468 seconds.