Thanks to N. Owad, I am obtaining the folowing Jones polynomial for the link under consideration
The corresponding Khovanov-Poincaré polynomial is
Using SnapPy with the following code
In[1]: LS=Link([[2, 24, 16, 1],[14, 4, 1, 5],[6, 15, 5, 16],[23, 6, 24, 7], [17, 14, 15, 13],[28, 22, 27, 23],[26, 13, 27, 12],[21, 25, 22, 28],[11, 26, 12, 25],[20, 8, 21, 7], [18, 10, 17, 11],[19, 20, 2, 3],[9, 18, 8, 19],[3, 4, 10, 9]])
In[2]: LSI1=LS.exterior()
In[3]: LSI1.volume()
Out[3]: 14.655
In[4]: LSI1.identify()
Out[4]: [L14n63195(0,0)(0,0)(0,0)(0,0)]
We identify the link as L14n63195.
It is worthwhile to note that the link under consideration is isomorphic to the following links
Please look at (Are the following two links isomorphic?)