The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  2  4  1  1  1  0  1  2  1  1  1  1  2  4  4  4  0  2  4
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  0 12  0  4  0  4  8  4  4 12 12  8 12  8  0  4  0  8 12  0  4 12  4  8 12  4  0  4  0  4  0
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  0  8  4  0  4  0  8  4  8 12  8  0  8  4 12 12  8  4  0  8 12 12  8  0  0  4  0  0  4 12  8
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8  0 12  4  0  4  8  0 12 12  4  8  4  8  8  0  8 12  0  4  4 12 12 12  0 12  0 12 12  0  0  0
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  8  0  8  0  8  8  0  0  8  8  8  8  8  0  0  8  0  0  0  8  8  8  8  0  0  8  8  0  0  8
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  8  0  8  0  0  8  8  8  8  8  0  0  0  0  0  8  0  8  0  0  8  0  8  8  0  8  8  8  8  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  8  8  0  0  8  0  8  8  0  8  0  8  8  8  0  0  8  8  8  0  8  0  8  0  0  8  8  0  8

generates a code of length 48 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+93x^40+20x^41+259x^42+120x^43+420x^44+336x^45+1309x^46+552x^47+2097x^48+552x^49+1252x^50+328x^51+359x^52+112x^53+184x^54+24x^55+81x^56+4x^57+65x^58+20x^60+3x^62+1x^68

The gray image is a code over GF(2) with n=384, k=13 and d=160.
This code was found by Heurico 1.16 in 1.21 seconds.