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

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

Homogenous weight enumerator: w(x)=1x^0+488x^44+156x^45+936x^46+660x^47+1489x^48+992x^49+1464x^50+560x^51+730x^52+164x^53+320x^54+28x^55+165x^56+32x^58+6x^60+1x^72

The gray image is a code over GF(2) with n=392, k=13 and d=176.
This code was found by Heurico 1.16 in 9.77 seconds.