The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1 12  2  1  1  1  1  2  1  1  1  2  8  1  1  4  1  1  1  1  0  1  2  1  1  2  1  1
 0  2  0  6  4 14 12  2  0  6 12 10  8 14 12  0  2 14  4 10  8  0  6  2 14 14  2 10 14  4  4  6 14  2  4  4  2  2 14 12  2  2 14  8  0  2 12  6 14  0  6  6 14
 0  0 12  0  4  4  0  4  0  8  0  8 12 12 12  8 12  8 12  0 12  4  0  0  4  8  0  0  8 12 12  8  4 12  0  0 12 12 12  0  4 12  8  0  8  8 12  0  8  8  0 12 12
 0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  0  0  0  0  0  8  8  0  8  0  8  0  8  0  8  8  8
 0  0  0  0  8  0  0  8  8  8  8  0  8  0  0  0  8  0  0  8  0  8  8  8  0  8  8  8  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  0  8  8  0
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  0  8  0  8  8  0  8  8  8  0  8  0  8  0  0  8  8
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  0  0  8  8  8  0  8  8  8  0  8  8  0  8  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  8  8  0  8  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+84x^46+80x^47+302x^48+304x^49+517x^50+1072x^51+916x^52+1696x^53+900x^54+1072x^55+530x^56+304x^57+208x^58+80x^59+80x^60+14x^62+23x^64+3x^66+3x^68+2x^70+1x^84

The gray image is a code over GF(2) with n=424, k=13 and d=184.
This code was found by Heurico 1.16 in 1.22 seconds.