The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+262x^47+714x^48+2078x^49+2180x^50+4372x^51+4130x^52+5774x^53+3925x^54+4204x^55+2201x^56+1802x^57+525x^58+344x^59+113x^60+74x^61+23x^62+30x^63+8x^64+3x^66+4x^67+1x^68

The gray image is a code over GF(2) with n=424, k=15 and d=188.
This code was found by Heurico 1.16 in 7.96 seconds.