The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+232x^43+872x^44+1504x^45+2005x^46+2606x^47+2437x^48+2336x^49+1944x^50+1238x^51+636x^52+328x^53+137x^54+58x^55+20x^56+8x^57+10x^58+10x^59+1x^60+1x^68

The gray image is a code over GF(2) with n=384, k=14 and d=172.
This code was found by Heurico 1.16 in 1.75 seconds.