2♣ is game forcing, 2NT showed 5-5 in the majors, X of 2NT was undiscussed but probably looked like interest in penalty, 3♣ did not have a definition, neither did the double of 3♣, X of 3♥ was penalty, 3♠ was probably preference, and now it's your turn.
Weak (10-13) NT is played by you and your partner, so partner knows you don't have that.
Double again, or..?
4NT is undiscussed.
Do you agree with both doubles?

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IMO
Agree with Lord Molyb's doubles.
LHO's 3♣ should be natural (XX = no preference, you choose, 3m = natural, 3M = preference)
The meaning of partner's double depends on the meaning of 3♣. But it should show interest in penalties.
Now Double = 10, 3N = 6, 4N = 4. And I like mr1303's small trump lead.