You must accept (because the mathematics is watertight and getting on for a century old) that there are fundamental limits to what a computer (Turing machine) can do. If the human mind is capable of such things, then it can't be simulated on a computer, no matter how powerful and how clever the programmer. It might (pure speculation) be possible to emulate the mind on a quantum computer, which is not subject to the same limitations.
Penrose has explicitly said that he is not claiming that there must be something non-physical about human consciousness. He accepts that it may one day be possible to emulate the human mind with a machine - but it is not possible to do it with a Turing machine, something more powerful would be needed.