No, it is not correct to entertain this belief, as demonstrated by a few specific instructions issued by the Congregation for the Doctrine of the Faith. In fact, their letter Declaratio de associationibus massonicis ("Declaration on Masonic Associations") was published in 1983 as a response to exactly this question.
It appears that the decision not to list the Masonic associations in the new Code was an editorial decision. Apparently the editors decided that if they listed specific groups, they might create the mistaken impression that only the groups in the list were forbidden. Instead, they decided to describe the groups more generally.
Here is the text of the (authorized English translation of the) letter:
DECLARATION ON MASONIC ASSOCIATIONS
It has been asked whether there has been any change in the Church’s decision in regard to Masonic associations since the new Code of Canon Law does not mention them expressly, unlike the previous Code.
This Sacred Congregation is in a position to reply that this circumstance is due to an editorial criterion which was followed also in the case of other associations likewise unmentioned inasmuch as they are contained in wider categories.
Therefore the Church’s negative judgment in regard to Masonic association remains unchanged since their principles have always been considered irreconcilable with the doctrine of the Church and therefore membership in them remains forbidden. The faithful who enrol in Masonic associations are in a state of grave sin and may not receive Holy Communion.
It is not within the competence of local ecclesiastical authorities to give a judgment on the nature of Masonic associations which would imply a derogation from what has been decided above, and this in line with the Declaration of this Sacred Congregation issued on 17 February 1981 (cf. AAS 73 1981 pp. 240-241; English language edition of L’Osservatore Romano, 9 March 1981).
In an audience granted to the undersigned Cardinal Prefect, the Supreme Pontiff John Paul II approved and ordered the publication of this Declaration which had been decided in an ordinary meeting of this Sacred Congregation.
Rome, from the Office of the Sacred Congregation for the Doctrine of the Faith, 26 November 1983.
Joseph Card. RATZINGER