There’s a lot more going on in that paper than an occasional reference to Penrose:
In this paper I argue that, contrary to Gödel’s assertion, his argument for the existence of “formally undecidable but intuitively true propositions” in the formal system of standard PA [Peano Arithmetic] (and other “systems” that are symbolically sufficient to formalise Intuitive Arithmetic recursively) is not clearly “constructive and intuitionistically unobjectionable”.
There’s a lot more going on in that paper than an occasional reference to Penrose: