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

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

Homogenous weight enumerator: w(x)=1x^0+50x^48+124x^49+373x^50+698x^51+830x^52+1344x^53+1752x^54+1974x^55+2352x^56+1992x^57+1592x^58+1258x^59+767x^60+584x^61+347x^62+162x^63+85x^64+44x^65+27x^66+4x^67+8x^68+8x^69+4x^70+3x^76+1x^78

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 4.25 seconds.