Is it within the code to teach redcaps (not Mercurian Magi) Parma Magica. After all, they are Magi of the order.
Bob
Moot.
The Parma Magica can only be learned by Gifted individuals, stated in the description of the ability on page 66 of the core book.
It is certainly within the code. The problem is that learning Parma requires the Gift, while virtually every Redcap is unGifted (Gifted ones are trained as Mercere magi instead).
What about someone - Redcap or not - who has Latent Magical Ability?
No. It requires the Gift, not a latent ability.
The only way it might be do-able is through an Initiation, and even that's something I wouldn't allow without a serious breakthrough. Parma Magica plays by its own rules (and more importantly, has a very specific place in the game setting as it stands).
An Initiation is an interesting idea, and might be the difficult goal of a magus' ongoing research.
Gaining Magic Might would serve the same end, more or less.
There might be research into a non-gifted version which only protects against the social effects of the gift. Or maybe just one that is easier to share (parma magica with target:group?) All kinds of ways you could go with research. Whether any of them will actually work or not...
imagine the frustration of some poor (hopefully NPC) bonisagus who has dedicated decades into researching a breakthrough only to find there is no way for it to work.
Overall, that's kind of the point of those big breakthroughs, isn't it?
It currently exists as a minor supernatural virtue, in RoP:M - it's called "Unaffected by the Gift" (I think.) As such, it's less Original Research, and more Integration.
Alternately, as a minor supernatural ability, it already can be Initiated, using the standard rules.
Strictly speaking, to answer the question, yes. It is within the Code for any legal mage of the Order to learn the Parma Magica.
This also allows for research into an alternative magic resistance for the non-Gifted, if any mage objects; "I am doing this research to protect Redcaps."
[Skimming along, I missed Ezzelino's answer, but I'll leave this one.]
This was the interpretation I was trying to ask about, but posting while tired, I wasn't clear enough. I was prompted to think by the breakthrough thread.
Bob
Alternately, of course (and to counter my previous point), it could simply be that nobody thought to develop an Initiation Script for it before now, and that there's nothing stopping the Cult of Heroes from giving every Redcap access to the Parma Magica in exchange for a minor flaw (Vow: Faithfully discharge my duties as a Redcap and a magus of House Mercere...)
It doesn't seem like there's any reason it shouldn't be possible to initiate (since Initiation rules are a newer system, and generally "requires the Gift" is old rules), except that it would have a major impact on the setting if it could be done and there would be much more incentive to seek exemptions to the rule about teaching the Parma to non-magi, such as Companions ("Hi, we just initiated a new Larta Magus!" " 
"), or to break that rule.