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

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

Homogenous weight enumerator: w(x)=1x^0+211x^44+296x^46+256x^47+564x^48+256x^49+240x^50+201x^52+8x^54+14x^56+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 22.1 seconds.