Did St. Augustine believe that Ezekiel 44:1-2 is a prophecy of Mary's perpetual virginity?

According to Roman Catholics and Orthodox Christians, Ezekiel 44:1-2 >And he brought me back to the way of the gate of the outward sanctuary, which looked towards the east: and it was shut. And the Lord said to me: This gate shall be shut, it shall not be opened, and no man shall pass through it: because the Lord the God of Israel hath entered in by it, and it shall be shut is a prophecy of the blessed Virgin Mary. They believe that this is not only a biblical belief but an historical one and claim that St. Augustine believed and taught that Ezekiel 44:1-2 is a prophecy of Mary, therefore confirming the perpetual virginity of Mary. Is this in any way true?