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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+28x^40+62x^41+79x^42+124x^43+159x^44+286x^45+295x^46+1192x^47+470x^48+2904x^49+489x^50+1104x^51+278x^52+264x^53+132x^54+120x^55+66x^56+58x^57+23x^58+20x^59+18x^60+10x^61+5x^62+3x^64+1x^66+1x^76

The gray image is a code over GF(2) with n=392, k=13 and d=160.
This code was found by Heurico 1.16 in 1.26 seconds.