Was St. Joseph alive when Jesus came to preach in his hometown?

We read how Jesus is rejected in his home-town, in Mtt 13:54-55 (NRSVCE): > He came to his hometown and began to teach the people in their synagogue, so that they were astounded and said, “Where did this man get this wisdom and these deeds of power? Is not this the carpenter’s son? Traditional teaching tells us that St. Joseph was already dead when Jesus embarked on his ministry. Joseph would have been a famous carpenter of the town, but not the only one in the profession. So, referring to the Late Joseph as “the carpenter” sounds incongruous. Note that the definitive article “the“ is peculiar to English whereas in some oriental languages, the part of verse reads as “that carpenter”. It is possible that St. Joseph was alive when these things happened? My question therefore is: **According to Catholic scholars, was St Joseph alive when Jesus came to preach in his hometown?**