The generator matrix

 1  0  1  1  1 14  1  2  1 12  1  1  1  1  8  1  1  0  1  1  1  1  4  0  6 10  6 10  0 14  6 12  1  1  1  1  2  2  4  2  6  1  1  1  1  1  1  2  1
 0  1 11  6 13  1 12  1  7  1 14  5  8  3  1  2  9  1  4 15 10  1  1  1  1  1  1  1  1  1  1  1  0 10 11 13  1  4  1  1  1 14  8  3  5 13 11 14  0
 0  0 12  0  4  4  8  4  4  8  4  0 12  8 12  4  0  0 12  8  8 12 12  8  0  0  0  0 12 12 12 12  0  8 12  4  4 12  4  8  8  4  4  8  8  0  0  4  8
 0  0  0  8  0  8  8  8  8  0  0  8  0  8  0  8  0  8  8  0  0  8  0  8  0  8  0  8  8  0  0  8  8  0  8  0  0  0  8  0  0  8  8  0  0  8  8  8  8
 0  0  0  0  8  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  0  0  8  0  8  8  0  8  8  0  0  0  0  0  0  8  0  8  0  8  8  0  8  0  0  8  0  0

generates a code of length 49 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+57x^44+230x^45+320x^46+534x^47+543x^48+782x^49+512x^50+572x^51+282x^52+150x^53+56x^54+30x^55+10x^56+2x^57+5x^58+2x^60+4x^61+2x^62+1x^66+1x^68

The gray image is a code over GF(2) with n=392, k=12 and d=176.
This code was found by Heurico 1.16 in 0.223 seconds.