The generator matrix

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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+69x^48+12x^49+218x^50+364x^51+612x^52+1660x^53+1130x^54+3324x^55+1633x^56+3364x^57+1118x^58+1668x^59+538x^60+340x^61+222x^62+20x^63+64x^64+15x^68+9x^72+2x^76+1x^84

The gray image is a code over GF(2) with n=448, k=14 and d=192.
This code was found by Heurico 1.16 in 3.1 seconds.