The generator matrix

 1  0  0  1  1  1 10  1  4  4  1  6  1  1  1  0 10  1  1 14  1  1  8  1  1 14  1  1  1  6 10  8  4 12 14  1  1 12 10  1  1  1  8  1  1  4  1  1 12  1  1  0  1
 0  1  0  2  1 11  1  0  6  1  1  1  4 13  3  1  4  6  5  1  4  7  1  8  6  1  7  7  8 14 10  1  1  1  1  1  1 14  1  5  2  8  1 14 13  6  5  7  1  6  6  1  3
 0  0  1  1  5  4  1  3  1 10  6  3  2  7  7  7  1  3 12  6  0  1  1  5  4  8  0 11 13  1  1  7 10  5  5 10  4  1 15  1 10 12  8 11  2  1 15 11 12 11 14  0  0
 0  0  0  4  4  0 12  8 12  4 12  8  8  0 12  4  4  0  8  4 12  0  8  4  4  8 12  0  0  8  4  0  8  0  0  0 12  8  8 12 12  4 12  4  8  4  0 12  0  4  8  8  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  8  8  8  0  8  8  8  0  0  0  0  8  8  8  0  0  8  8  8  8  8  8  8  8  0  0  8
 0  0  0  0  0  8  8  0  0  0  8  8  8  8  8  8  0  0  8  0  8  0  0  8  0  8  0  8  8  0  8  0  0  8  0  0  0  0  8  8  8  0  0  0  8  8  0  8  0  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+187x^46+596x^47+1813x^48+3228x^49+4903x^50+7652x^51+9031x^52+10828x^53+8956x^54+7812x^55+5069x^56+3060x^57+1410x^58+508x^59+275x^60+100x^61+53x^62+8x^63+29x^64+11x^66+6x^68

The gray image is a code over GF(2) with n=424, k=16 and d=184.
This code was found by Heurico 1.16 in 30.9 seconds.