Jesus never wrote anything, but He did build a Church. He gave it the keys to lose and bind on earth and in Heaven, and the authority to forgive sins, and promised it the Holy Spirit to lead it to all truth, and that the gates of hell would not prevail against it. Yes, scripture is the heart of the Church. But rip the heart out of the body in which Christ intended it to be nurtured and taught, and that heart will not accomplish what the Lord intended of it, as the 30,000 bickering and opposing sects prove.
John 8:6 "But Jesus stooped down and wrote on the ground with His finger". He was literate(unlike Mohammed) and did write.
And we are worlds apart on what was meant when Jesus spoke to Peter. But your Church will interpret it to mean they have the POWER and AUTHORITY to do whatever.
IF He had done that, He would have spelled out exactly to whom was given this authority. The Catholic Church is not mentioned in the Bible anywhere. It would be quite a stretch for them to claim all of this power is theirs. You've not proven the Catholic Church has anything to do with this verse.