The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+49x^44+126x^45+314x^46+628x^47+995x^48+1438x^49+2896x^50+3012x^51+4841x^52+4016x^53+5190x^54+2976x^55+2891x^56+1432x^57+887x^58+488x^59+257x^60+146x^61+79x^62+60x^63+20x^64+10x^65+9x^66+4x^67+1x^68+1x^70+1x^72

The gray image is a code over GF(2) with n=424, k=15 and d=176.
This code was found by Heurico 1.16 in 15.1 seconds.