The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+302x^48+942x^49+1589x^50+2198x^51+2188x^52+2480x^53+2148x^54+1790x^55+1228x^56+870x^57+382x^58+134x^59+68x^60+24x^61+24x^62+6x^63+1x^64+4x^65+1x^66+4x^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 2.08 seconds.