The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+342x^48+870x^49+1611x^50+1958x^51+2603x^52+2344x^53+2267x^54+1618x^55+1358x^56+648x^57+435x^58+202x^59+65x^60+24x^61+13x^62+14x^63+5x^64+2x^65+2x^66+2x^68

The gray image is a code over GF(2) with n=424, k=14 and d=192.
This code was found by Heurico 1.16 in 2.22 seconds.