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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+57x^44+68x^45+156x^46+172x^47+302x^48+412x^49+461x^50+632x^51+1233x^52+1888x^53+3453x^54+4992x^55+5078x^56+5000x^57+3476x^58+2026x^59+1187x^60+628x^61+507x^62+316x^63+249x^64+156x^65+117x^66+44x^67+72x^68+40x^69+19x^70+8x^71+10x^72+2x^74+2x^75+2x^76+1x^78+1x^84

The gray image is a code over GF(2) with n=448, k=15 and d=176.
This code was found by Heurico 1.16 in 22.5 seconds.