The generator matrix

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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+57x^46+102x^47+283x^48+278x^49+690x^50+634x^51+1957x^52+1494x^53+4837x^54+2592x^55+6884x^56+2674x^57+4890x^58+1500x^59+1913x^60+592x^61+710x^62+262x^63+188x^64+70x^65+68x^66+26x^67+33x^68+10x^69+11x^70+4x^71+4x^72+2x^73+1x^76+1x^78

The gray image is a code over GF(2) with n=448, k=15 and d=184.
This code was found by Heurico 1.16 in 18.2 seconds.