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

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

Homogenous weight enumerator: w(x)=1x^0+201x^44+232x^46+256x^47+693x^48+256x^49+208x^50+182x^52+8x^54+9x^56+1x^60+1x^88

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 0.125 seconds.