The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^41+358x^42+380x^43+1026x^44+1072x^45+2018x^46+1868x^47+3018x^48+1872x^49+2030x^50+932x^51+858x^52+368x^53+288x^54+84x^55+112x^56+28x^57+8x^58+8x^60+2x^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 3.31 seconds.