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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+146x^49+428x^50+716x^51+1154x^52+1682x^53+2662x^54+3202x^55+4494x^56+3964x^57+4510x^58+3262x^59+2581x^60+1488x^61+1156x^62+632x^63+310x^64+196x^65+74x^66+58x^67+33x^68+10x^69+2x^70+2x^71+3x^72+2x^73

The gray image is a code over GF(2) with n=456, k=15 and d=196.
This code was found by Heurico 1.16 in 15.7 seconds.