Even as it’s used in English to modify “information,” either as a single one-word attributive adjective or as a single hyphenated one, I think “code[-]word” could use some help to capture more coherently the [sensitive] nature of that information.

I say this primarily because, in addition to the one you describe, I see another possible attributive use of “code[-]word” in “code[-]word information” as meaning simply/literally “information about code words,” such as a list of code words (with or without their corresponding projects/operations) currently or formerly in use by a/n [spy] agency
(cf: the attributive use of “login” or “credit card” in “Never reveal your login/credit card information!”).

In English, to distinguish it better in my mind from the “login/credit card” attributive use just mentioned above, I read “code[-]word information” in the attributive use at issue to mean either “code[-]word[-]protected information” or “code[-]word level information,” with both of which standing for “information requiring code[-]word clearance to access” and with this in mind, I’d humbly propose that it would require more than adding a simple proposition in French to coherently transform the noun “mot-code” to an attributive adjective of “information.”

Although with nothing to support me, I do think, however, that “mot-code” alone could coherently modify words like “niveau” or “habilitation” (just as I’ve used “code[-]word” to modify “level” and “clearance” in English) and perhaps even a word like “genre” (which is actually my favorite):

Renseignements/informations [d’un/du] niveau mot-code classifié(e)s/classé(e)s très secret/[très secret défense].

Renseignements/informations [d’une] habilitation mot-code classifié(e)s/classé(e)s très secret/[très secret défense].

Renseignements/informations [du] genre mot-code classifié(e)s/classé(e)s très secret/[très secret défense].