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

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

Homogenous weight enumerator: w(x)=1x^0+256x^44+1534x^48+256x^52+1x^96

The gray image is a code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 4.96 seconds.