The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+26x^40+168x^41+222x^42+524x^43+605x^44+1358x^45+1873x^46+2072x^47+2791x^48+2136x^49+1831x^50+1210x^51+616x^52+520x^53+144x^54+150x^55+54x^56+40x^57+18x^58+10x^59+3x^60+2x^61+7x^62+2x^63+1x^66

The gray image is a code over GF(2) with n=384, k=14 and d=160.
This code was found by Heurico 1.16 in 3.39 seconds.