The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 14  2  1  1  8  1  1  1  4  1 10  1  1  1  6  1  0  1  1  1  1  1  1  1  1 10 12 14  1  1  1  2  1  1 12  1  1  1  0  1 14  1
 0  1 11  6 13  1 12  7  1 10  1  1  1  8  3  1  5 14 15  1  4  1  2  9 10  1  5  1  8 11  9  7  3 13  6  4  1  1  1 12 15 10  4  8  9  1  4  4 14  1  3  1  3
 0  0 12  0  4  0  0  4  8  8  4 12 12  4  8  4  8  4  0  4  4  8  4  0  0  0  8  8 12  4  0 12  0 12  8 12  8  8  4  0  0  8 12 12  0  0 12  4 12  0  0  4  0
 0  0  0  8  0  0  0  0  8  0  8  8  0  8  8  0  0  8  0  8  0  0  0  8  8  8  8  8  8  8  0  8  8  0  0  8  0  0  0  8  0  0  0  0  8  0  8  8  8  8  0  8  8
 0  0  0  0  8  0  0  8  0  0  0  0  0  8  0  8  0  8  8  8  8  8  0  8  8  0  8  0  0  8  8  8  8  0  8  0  0  8  0  0  0  0  8  8  8  0  0  0  0  8  8  0  0
 0  0  0  0  0  8  0  8  0  8  8  0  0  0  8  8  8  0  0  8  8  0  0  0  8  8  0  0  0  8  8  0  8  8  0  8  0  8  8  0  0  0  8  0  8  8  8  0  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  8  8  8  0  8  0  8  0  8  8  8  8  8  8  8  0  0  8  0  8  0  0  0  0  8  0  8  8  0  0  8  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+85x^46+104x^47+365x^48+880x^49+1036x^50+2088x^51+2170x^52+3040x^53+2064x^54+2168x^55+1078x^56+816x^57+219x^58+120x^59+77x^60+36x^62+13x^64+13x^66+5x^68+3x^70+3x^72

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 2.89 seconds.