The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+40x^41+156x^42+326x^43+724x^44+1066x^45+2160x^46+2196x^47+3108x^48+2138x^49+2313x^50+1060x^51+574x^52+258x^53+121x^54+52x^55+34x^56+14x^57+15x^58+14x^59+6x^60+4x^61+3x^62+1x^64

The gray image is a code over GF(2) with n=384, k=14 and d=164.
This code was found by Heurico 1.16 in 2.52 seconds.