The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+520x^44+1056x^46+1226x^48+720x^50+384x^52+144x^54+36x^56+8x^60+1x^64

The gray image is a code over GF(2) with n=384, k=12 and d=176.
This code was found by Heurico 1.16 in 70.9 seconds.