The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^40+312x^41+633x^42+1544x^43+2758x^44+4728x^45+7278x^46+9760x^47+11286x^48+9910x^49+7386x^50+4764x^51+2727x^52+1406x^53+520x^54+264x^55+94x^56+58x^57+21x^58+20x^59+7x^60+2x^61+2x^62

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 32.4 seconds.