Is Robinson arithmetic the weakest incompletable system of arithmetic?

Question

Robinson arithmetic (Q) is weaker than PA. We know that any theory that interpret Robinson arithmetic will be incomplete as well. It seems Robinson found his axioms noting what was necessary to conclude the incompleteness proof. But what if there is some very strange axiom system we don't really think that is connected to arithmetic, weaker than Q, and still incompletable in the sense any other theory interpreting it will also be incomplete? Is this possible? Can we say that Q is the weakest system?