The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+134x^41+385x^42+878x^43+1493x^44+2430x^45+3999x^46+4182x^47+5795x^48+4386x^49+3858x^50+2458x^51+1454x^52+690x^53+324x^54+146x^55+80x^56+32x^57+9x^58+16x^59+9x^60+8x^61+1x^62

The gray image is a code over GF(2) with n=384, k=15 and d=164.
This code was found by Heurico 1.16 in 9.03 seconds.