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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+25x^46+64x^47+121x^48+166x^49+161x^50+350x^51+207x^52+784x^53+762x^54+2156x^55+1799x^56+3180x^57+1818x^58+2196x^59+788x^60+816x^61+197x^62+288x^63+111x^64+158x^65+81x^66+62x^67+27x^68+16x^69+20x^70+4x^71+15x^72+4x^74+2x^76+4x^78+1x^80

The gray image is a code over GF(2) with n=456, k=14 and d=184.
This code was found by Heurico 1.16 in 6.4 seconds.