The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+140x^41+522x^42+1326x^43+2985x^44+5344x^45+7021x^46+10030x^47+10570x^48+10208x^49+7550x^50+5392x^51+2434x^52+1148x^53+537x^54+158x^55+89x^56+36x^57+18x^58+6x^59+15x^60+4x^61+2x^64

The gray image is a code over GF(2) with n=384, k=16 and d=164.
This code was found by Heurico 1.16 in 27.2 seconds.