Does Roman Catholic doctrine teach that Christ no longer has a body that possesses flesh? Does Roman Catholic doctrine teach that Christ's incorruptible body no longer has flesh?

I was translating a work of John of Damascus entitled Περὶ τοῦ ἀχράντου σώματος, οὗ μεταλαμβάνομεν. In this work, John is quoting (actually, he seems to be paraphrasing) a statement made by Gregory Nazianzen in his work entitled in English, "The Oration on Holy Baptism."

Here is John's quotation in Greek.


  Πίστευε Χριστὸν τὸν Υἱὸν τοῦ Θεοῦ ἥξειν πάλιν μετὰ τῆς ἐνδόξου αὐτοῦ παρουσίας κρῖναι ζῶντας καὶ νεκρούς· οὐκέτι μὲν σάρκα, οὐκ ἀσώματον δὲ, οἷς οἶδεν αὐτὸς λόγους, θεοειδεστέρου σώματος, ἵνα καὶ ὀφθῇ ὑπὸ τῶν ἐκκεντησάντων, καὶ μείνῃ Θεὸς ἔξω παχύτητος.


What Gregory Nazianzen writes is translated in English as (sec. 45), 


  Believe [that for us sinners He was led to death; was crucified and buried, so far as to taste of death; and that He rose again the third day, and ascended into heaven, that He might take you with Him who were lying low; and that] He will come again with His glorious Presence to judge the quick and the dead; no longer flesh, nor yet without a body, according to the laws which He alone knows of a more godlike body, that He may be seen by those who pierced Him, and on the other hand may remain as God without carnality.


Gregory clearly states that Christ does not possess flesh. The Greek is οὐκέτι μὲν σάρκα, "no longer flesh."

This is the basis for my question.
I don't understand how a body can exist without flesh, But a simple answer to your question is NO, It does not. It is actually the opposite. It is condemned as a heresy in the Catholic Church if one claims that Jesus is in heaven without his body/flesh. This concept falls into variation of different heresies Docetism, Apollinarism, Manichaeism etc.,

Catholics believe that Jesus is present with his flesh in Eucharist. And he is present in the Eucharist as he is present in the Trinity, i.e, with his flesh but his glory hidden to naked eye.

UPDATE:

In Luke 24:39, Jesus himself says that he has σάρκα That should end the discussion whether Jesus has σάρκα or not.

With regards to what the Catholic Church teaches, I think what St. Gregory Nazianzen was saying here with respect to "Flesh" is not to be taken as the nature of flesh but fallen state of flesh. In Jesus's second coming, he is going to come with a body that is not bound by natural laws. That is he is not going to fall to earth because of gravity. Christ's body after Resurrection is "of the same nature, but differed in glory." St. Thomas Aquinas in his Summa Theologica answers the question of Whether Christ's body rose again entire(with flesh and bones)?:


  Flesh and blood are not to be taken there for the nature of flesh and blood, but, either for the guilt of flesh and blood, as Gregory says [Pope St. Gregory, Moral. in Job 14:56, or else for the corruption of flesh and blood: because, as Augustine says (Ad Consent., De Resur. Carn.), "there will be neither corruption there, nor mortality of flesh and blood." Therefore flesh according to its substance possesses the kingdom of God, according to Luke 24:39: "A spirit hath not flesh and bones, as you see Me to have." But flesh, if understood as to its corruption, will not possess it; hence it is straightway added in the words of the Apostle: "Neither shall corruption possess incorruption."