The generator matrix

 1  0  1  1  1 14  1  2  1 12  1  1  1  1  8  1  1  4  1  1  1  1  0 12  6 10  6 10  0  8 14  2 14  1  1  1  1  6  8  1  1  6  1  1  2  6 10  4
 0  1 11  6 13  1 12  1  7  1 14  5  8  3  1  2  9  1  4  1 10 15  1  1  1  1  1  1  1  1  1  1  1  0  5  3 12  1  1  7  6  1 10 13  1  1  1  1
 0  0 12  0  4  4  8  4  4  8  4  0 12  8 12  4  0 12 12 12  8  8  0  8  0  0  0  0 12  4  4 12  8  0  8  8  0  8 12  4  0 12  0  4  0 12  8 12
 0  0  0  8  0  8  8  8  8  0  0  8  0  8  0  8  0  0  8  8  0  0  8  8  0  8  0  8  8  8  0  0  8  8  0  8  0  0  8  0  0  8  0  0  0  0  0  8
 0  0  0  0  8  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  0  0  8  0  8  8  0  8  0  0  8  8  0  0  8  8  0  0  8  0  0  8  0  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+345x^44+192x^45+578x^46+576x^47+734x^48+576x^49+572x^50+192x^51+313x^52+2x^54+7x^56+6x^60+2x^72

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 58 seconds.