The generator matrix

 1  0  1  1  6  1  1  1  4  1  1  4  2  1  1  1 14  1  1 10  1  1  1  1  8  1  1  2  1  1  1  6  1  0  0  1  1  1 14  1 14  4  1  0  2 12  1 12  6  1  1  1  2
 0  1  1  6  1  3  5  4  1  7  2  1  1  9  8  3  1 14 15  1  6  7  8  9  1 10  5  1  4 11  0  1 14  1  1 11  1 11  1 12  1  1  1  4 14  1  0  8  1  2  7 11  4
 0  0  2  0  0  0  0  2  2  2 10  4  2  8  4 14 12  4  8  6  6 12  2 14  2  6  6 12 12 12  6  6 12 14  0 12 10  2 12  6  2 10 10  2 10  6 12  2 14 10 12  0 10
 0  0  0  8  0  0  0  0  0  0  0  0  8  8  0  8  0  0  0  8  8  8  0  8  8  0  0  8  8  0  8  8  0  0  8  0  8  8  8  8  0  0  8  8  0  0  8  8  0  8  0  0  0
 0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  0  0  8  0  0  8  0  8  8  8  0  0  8  8  0  8  8  8  8  0  0  8  0  8  0  8  0  8  8  0  8  8  0  8  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  0  8  8  8  0  8  0  8  8  0  8  0  0  8  8  8  0  0  8  0  8
 0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  8  0  8  8  8  0  8  8  8  8  0  8  0  0  0  8  0  0  0  8  8  0  0  0  0  8  0  0  0  8  0  8  8  0  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+156x^46+348x^47+1028x^48+1304x^49+2893x^50+3248x^51+5205x^52+4616x^53+5167x^54+3224x^55+2889x^56+1192x^57+803x^58+336x^59+199x^60+56x^61+63x^62+12x^63+14x^64+4x^66+8x^68+2x^70

The gray image is a code over GF(2) with n=424, k=15 and d=184.
This code was found by Heurico 1.16 in 10.2 seconds.