The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+106x^44+224x^45+343x^46+530x^47+621x^48+652x^49+588x^50+412x^51+239x^52+144x^53+91x^54+66x^55+48x^56+20x^57+1x^58+9x^60+1x^74

The gray image is a code over GF(2) with n=392, k=12 and d=176.
This code was found by Heurico 1.16 in 0.344 seconds.