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  2  4  1  1  2  4  1  1  2  4  2  4
 0 12  0  0  0  4 12 12  8  8  0  0  4  4  4 12  0  8  4 12  4  0  8  8  8 12 12  4  4  0  0  4  4  4 12  4  4  4  0  0 12 12  8  8  8  8  0  0
 0  0 12  0  4  4  4  0  8  0  4 12  4  4  0  8  0  8 12  4  8  0 12  0  4 12  4  8  8  4 12  0  0  8  8  0  0  8  4  4  0  8  4  4 12 12 12 12
 0  0  0 12  4  8  4  4  0  4  4  0  0 12  4  8  0 12  4 12  4  4  8  0  8  8  0  0  8 12 12  4 12 12  8  0 12  4  8  0  8  0 12 12 12 12  8  0
 0  0  0  0  8  8  0  8  8  8  0  8  0  8  0  8  8  8  0  8  0  0  8  0  0  8  0  8  0  0  8  8  8  0  0  8  0  8  8  0  0  8  0  8  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+276x^44+352x^46+813x^48+352x^50+240x^52+12x^60+1x^64+1x^80

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 19.5 seconds.