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  2  2  1  1  2  1  2  2  2  4  8  1  1  2  1  2  2  1  4  2  2  1  1  2  1  1  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  8 12  0  4  4  0  4  8  0  8  0  4 12  4  8  4  4  4  0 12  4  4  4  0  8 12  8  0  4  4 12  4  8  8 12 12  4  8  8
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4  0  4 12  8  4  0 12 12  0  4  4  8 12  4 12  8 12 12  8  8  8  0  8  8 12 12  4  4  4  8 12 12  4  0  4  8 12  8  8
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  8  4 12  8  0  0  0  0  4  4  4 12  4 12  0  8  4  8  4  4  0  4 12 12  0  8  4  4  4 12  0  4  0 12  0  8  0 12  4 12
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  8  0  8  8  0  8  8  0  8  8  0  8  8  0  0  0  8  0  0  8  8  0  8  8  8  8  8  0  8  8  8  8  8  0  8  8  0  8  8  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  0  0  0  0  0  8  0  0  0  8  0  8  8  0  8  8  8  8  8  8  8  8  0  8  0  0  8  8  8  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  0  8  0  8  8  8  8  0  0  0  8  8  8  0  8  0  0  0  8  8  8  8  0  8  0  8  0  8  0  8  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  8  8  0  8  8  8  8  0  8  0  8  8  0  8  8  0  8  0  8  8  0  0  8  0  8  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+59x^46+74x^47+146x^48+238x^49+299x^50+308x^51+436x^52+616x^53+1669x^54+2874x^55+2949x^56+2942x^57+1769x^58+510x^59+425x^60+322x^61+229x^62+180x^63+108x^64+92x^65+50x^66+22x^67+26x^68+14x^69+19x^70+3x^72+1x^74+1x^76+1x^80+1x^82

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 6.2 seconds.