The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+121x^48+458x^49+800x^50+1162x^51+1102x^52+1108x^53+1139x^54+1012x^55+634x^56+406x^57+104x^58+62x^59+35x^60+12x^61+13x^62+4x^63+10x^64+6x^66+1x^68+2x^70

The gray image is a code over GF(2) with n=424, k=13 and d=192.
This code was found by Heurico 1.16 in 0.822 seconds.