The automorphism group of the countable atomless Boolean algebra does not have ample generics

Question

I was told that the automorphism group of the countable atomless Boolean algebra does not have ample generics. I assume that one would show this by using the Fraisse-theoretic characterizations of countable ultrahomogeneous structures with automorphism groups with ample generics by means of finite structures expanded with $n$ partial automorphisms for $n < \omega$. However, I have not been able to find any reference for this fact. What would be a good reference? I would also be grateful for the summary of the argument if it can be sketched here.