The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+84x^40+366x^41+804x^42+1580x^43+2940x^44+4842x^45+7343x^46+9130x^47+11095x^48+9788x^49+7255x^50+4708x^51+2766x^52+1438x^53+823x^54+322x^55+132x^56+74x^57+23x^58+4x^59+6x^60+4x^61+6x^62+2x^66

The gray image is a code over GF(2) with n=384, k=16 and d=160.
This code was found by Heurico 1.16 in 32.3 seconds.