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

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

Homogenous weight enumerator: w(x)=1x^0+46x^46+94x^47+136x^48+182x^49+249x^50+380x^51+554x^52+894x^53+1797x^54+2554x^55+2712x^56+2606x^57+1731x^58+894x^59+546x^60+294x^61+202x^62+144x^63+123x^64+100x^65+67x^66+30x^67+18x^68+20x^69+2x^70+4x^72+1x^74+2x^76+1x^86

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 6.09 seconds.