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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+78x^46+326x^47+622x^48+936x^49+1295x^50+1688x^51+2193x^52+2404x^53+2074x^54+1682x^55+1289x^56+772x^57+395x^58+254x^59+179x^60+108x^61+59x^62+16x^63+4x^64+4x^65+2x^66+2x^67+1x^70

The gray image is a code over GF(2) with n=424, k=14 and d=184.
This code was found by Heurico 1.16 in 3.77 seconds.