I'm not a lawyer but "codice fiscale" is not PHI. The Italian Data Protection Authority puts codice fiscale under PII[0] and it's not mentioned in the PHI section[1,2,3,4].
[0] https://www.garanteprivacy.it/home/diritti/cosa-intendiamo-p...
[1] https://www.garanteprivacy.it/temi/dati-sanitari
[2] https://www.garanteprivacy.it/faq/fascicolo-sanitario
[3] https://www.garanteprivacy.it/faq/referti-online
[4] https://www.garanteprivacy.it/web/guest/home/docweb/-/docweb...
[edit: formatting]