The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+98x^39+298x^40+626x^41+1051x^42+2066x^43+2511x^44+5026x^45+5973x^46+10600x^47+8897x^48+10534x^49+6181x^50+5374x^51+2560x^52+1806x^53+887x^54+572x^55+208x^56+112x^57+72x^58+40x^59+21x^60+8x^61+12x^62+2x^63

The gray image is a code over GF(2) with n=384, k=16 and d=156.
This code was found by Heurico 1.16 in 51 seconds.