The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  2  1  1  1 12  1  1  1  1  8  1  1  1  2  1  4  1  1  1  2  1  1  4  1  1  1  2  1
 0  2  0  6  4 14 12  2  0  6 12 10  8 14  0 12  6  6  2  8 14  2  2  2  2  6  2 12  8  2  2 14 12 10  8  2 14 10  6  6  6 14  2  0 12  4  6  6
 0  0 12  0  4  4  0  4  0  8  0  8 12 12  8 12  4  8  0 12  4  4  8  4  0  8  4  8 12 12 12  8  8  0  0  4 12  4  0  0  8  8 12  0  8  4  8  0
 0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  8  0  8  8  8  0  8  8  0  8  8  0  0  0  8  0  8  0  8  8  0  0  8  0  8  0  8
 0  0  0  0  8  0  0  8  8  8  8  0  8  0  0  0  8  8  8  0  8  0  8  8  0  0  8  0  8  0  0  8  8  8  8  0  0  0  8  0  0  0  0  8  0  0  8  8
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  0  0  8  0  8  0  0  0  8  0  8  8  0  8  8  8  0  8  8  8  8  0  0  8  0  0  8  8  0  8  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  8  8  0  8  0  0  8  8  8  8  8  8  0  8  0  0  0  0  8  8  0  0  8  8  0  0  8  0  0  0  8  8  8  8  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+46x^41+138x^42+184x^43+255x^44+636x^45+807x^46+1464x^47+1228x^48+1442x^49+782x^50+610x^51+230x^52+162x^53+104x^54+38x^55+10x^56+16x^57+24x^58+6x^59+2x^60+2x^61+1x^62+2x^63+1x^64+1x^76

The gray image is a code over GF(2) with n=384, k=13 and d=164.
This code was found by Heurico 1.16 in 25 seconds.