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  1  1  1  2  2  1  1  2  2  1  1  4  2  8  4  2  0  1  2  1  4  0  1  4  1  4  0  2  2  2  2  1  1
 0 12  0  4  0  0  4 12  0  8  4  0  4  8  4  4  0  8  0  4 12  0  4  4  8  0  0 12  8 12  8  4  0 12  4  4  4  8  4  8  4 12  4 12  4  4 12 12  0  0 12 12 12 12  0  8
 0  0 12  4  0 12  4  0  0  4  0  8 12 12  8  4  8  4  4  4  0  8  4  0  4 12 12  8  8 12  4 12 12  4  4 12  4  4  4  4  8  0  4  8  0  4  0  8 12  4  0  8  4  4 12  4
 0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  0  0  0  8  8  0  8  8  0  8  0  8  0  8  0  8  8  0  0  8  8  8  0  8  0  8  0  8  8  8  0  8  0  8  8  8  0  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  0  8  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  8  0  0  0  0  8  8  0  0  8  0  8  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  8  8  8  8  8  0  0  0  8  0  0  0  8  8  8  0  8  0  8  0  8  0  0  8  8  8  8  8  8  8  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  0  8  0  8  0  8  0  8  8  8  0  0  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  0  0  8  8  8  0  0  8  8  8  8
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  0  0  8  8  8  0  0  8  0  8  0  8  8  8  0  0  0  0  8  8  0  8  8  0  8  8  0  0  8  0  8  8  8  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  0  0  8  8  0  0  0  8  0  8  0  8  8  8  8  8  8  8  8  8  0  0  8  0  8  8  8  0  8  0  8  8  8  8  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+99x^46+305x^48+80x^49+451x^50+308x^51+991x^52+928x^53+1984x^54+1728x^55+2645x^56+1760x^57+2013x^58+1000x^59+923x^60+288x^61+424x^62+32x^63+210x^64+16x^65+125x^66+4x^67+37x^68+20x^70+7x^72+3x^74+1x^76+1x^78

The gray image is a code over GF(2) with n=448, k=14 and d=184.
This code was found by Heurico 1.16 in 6.83 seconds.