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

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

Homogenous weight enumerator: w(x)=1x^0+101x^50+216x^52+360x^54+128x^55+891x^56+768x^57+880x^58+128x^59+345x^60+140x^62+67x^64+49x^66+14x^68+4x^70+1x^72+2x^74+1x^92

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 0.584 seconds.