The generator matrix

 1  0  1  1  1 14  1  1  0 14  1  1  1  0  1  2  1  1  1 14  1  1  6  1  1  1  8  1 14  1  1  1 10  1  1  2  8  1  1  1 14  1  1  1  1  2  1  1  4 12  1  2  1
 0  1 11  6  1  1  8  3  1  1 14  9  6  1  3  1 13  0 14  1  5  6  1 13 11 12  1 11  1  6 12 13  1 10 15  1  1  4  5 12  1  1 14 10  2  1  9  3  1  2 13  1  8
 0  0 12  0  0  0  0  8 12  4  4  4 12 12  0  4  8 12 12  8  4  0  8  4  8  8  0  4 12  0 12 12  8  4  4  0  0  0  8  8 12  0  8 12  8 12  0  4  0  4 12  4  0
 0  0  0 12  0  0  8  8  8  8  0  8  8 12 12 12 12  4 12  4 12 12  4  4 12 12  4  8  0  8  0  8  0  4 12 12 12 12  4  0  4 12  4  8 12  8  4  4 12  0  4  8  4
 0  0  0  0  4 12 12  8  4  0  0  4  4  8 12  4  0  8  4  0  8  4  4  4  8  4  0  4  4  4 12  0  0  0  8  0  4  0  4  8  4  8  0 12  4  4  8  8  8  4  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+35x^46+156x^47+370x^48+828x^49+1070x^50+2134x^51+2393x^52+2548x^53+2437x^54+2076x^55+982x^56+792x^57+293x^58+120x^59+44x^60+20x^61+26x^62+24x^63+15x^64+4x^65+9x^66+2x^67+3x^68+2x^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 2.86 seconds.