The generator matrix

 1  0  1  1  1 14  1  4  1 10  1  1  2  1  1  1  1  1 14  1  1  4  4  1  1  8  1  0  1  1 10  1 12  6  1  1  1  1  1  1  1  1  2  1  2  0  1  1  2  1  1  4  4
 0  1  1  0  7  1  2  1 11  1  5 14  1  3 14  9  8  3  1  6 12  1  1  9  1  1 15  1 10 14  1 13  1  1  3 10 15 11  0  6 14 13  2  6 14  1  2 10 12 13  6  1  1
 0  0  2  6  2  4 14  2  0  6  4  0 12 12  6  4  0  6 10  4  2 14  0 14  4  8 14 14  4  2  8  4 12 10  2  0  0 10  2  0 14 10 10  8 14  8  0 10  2 10  8 14  2
 0  0  0 12  0  0 12  8 12  0 12  4  0 12  4  4 12  0  8 12  4 12 12  8  0  4 12  8  4  8  8  0 12  4 12  0  8  8  0 12  0 12 12  8  4  8  8  4  0  8 12  4  8
 0  0  0  0  8  0  8  8  0  0  8  0  8  0  8  8  8  8  0  0  0  8  8  8  8  8  8  0  8  8  8  0  8  0  0  8  0  0  0  8  0  8  0  8  0  8  8  8  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  8  8  8  0  8  8  0  8  8  8  8  8  0  8  8  0  8  8  8  8  8  0  8  0  0  0  8  8  0  0  0  0  8  8  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+188x^46+328x^47+853x^48+1520x^49+2549x^50+3540x^51+5031x^52+5132x^53+4689x^54+3584x^55+2598x^56+1400x^57+705x^58+292x^59+192x^60+76x^61+43x^62+24x^64+18x^66+5x^68

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 10.3 seconds.