A popular way to play a 3NT opening is to show a 7- or 8-card solid minor with no outside Ace or King, or otherwise with little outside.
One problem here is that you have likely wrong-sided the 3NT contract. You'd like the lead to come around to the player who has values in the side suits.
Another problem is that the bid won't come up very often. With a solid 7-card minor your average total point count will be 13-14 HCP, so you'll likely have some values on the side. My preference is that the bid shows 12-15 HCP. This will come up more, the contract is more likely to be successful and the hand type is still difficult to manage with standard methods.
Gambling Three Notrump
Re: Gambling Three Notrump
Which reminds me, I remember once when RHO opened 1NT I had a running 7-card club suit and nothing else. I doubled, redoubled, all pass. Fun times.