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I remember one episode from The X-Files (I think) where aliens contacted people.

They were using weird language and people were trying to decode it to understand what they want. I remember that they have their spaceship hidden in the ocean or something and in the final scenes, (I don't remember why) people decided to nuke them and when it was too late someone has decrypted their message which said that "they're coming in peace" (and then was the nuke explosion and probably end of the episode).

I don't really remember if it was The X-Files, or another sci-fi movie, but I remember the alien in the monitor was similar to the ones from The X-Files (big head with big eyes).

This is probably the Outer Limits episode "Trial By Fire"

From the Wikipedia synopsis:

En route to his Inauguration Ball, newly sworn-in President Charles Halsey, his campaign slogan "Let me be your friend", is diverted to a nuclear bunker and is greeted by his predecessor's staff including Junior Science Advisor Janet Preston; National Security Advisor Tarquin; and General Covington, commander of the U.S. space program. They inform the president that an object traveling at half the speed of light will impact Earth in thirty minutes with the potential to wipe out most life on Earth.

...

As the fleet settles into orbit around Earth, another satellite receives a signal from the aliens. NASA contacts the bunker to say that they have discovered a video/audio message within the signal, and relays the message to the bunker. The message shows a humanoid alien making an unintelligible speech.

..

After an alien response is broadcast, one of the orbiting ships breaks formation and enters the atmosphere, landing in the Pacific Ocean. The president, shaken by the prospect of invasion, is unable to make a decision. Despite pleas by the scientists and Elizabeth, Halsey orders the military to DEFCON 2; the Russians mobilize their nuclear forces to strike any further alien incursions. Some of the scientists speculate that the aliens live in a water-based environment which alarms the military who infer that the aliens are intent on an invasion in order to gain control of Earth's oceans.

Here we see the 'ship underwater' notion you remember.

Succumbing to panic, Halsey orders an immediate response using the space shuttle's nuclear device. At the same time, the Russians launch their missiles at the fleet from submarines in the Bering Sea.

In the final moments before the objects arrive, a teleprinter message comes through from the cryptanalysts, having decoded the alien's original message. They realize that the aliens do in fact live in a liquid environment and that they were speaking in plain English. Having removed the liquid distortion from the message, Preston solemnly informs him of what the original transmission said: "Let us be your friends." As the occupants of the bunker prepare to meet their fate, Halsey, regretting all that he has done alongside the military officials, and his wife mournfully embrace.

The aliens do in fact resemble Grays, although with a certain aquatic vibe to go with the particulars of the episode plot.

Of course this is not the X-files, but one of the hallmarks of the X-Files is that alien contacts are typically not known about by anyone other than the main characters (and at that, usually never in a direct, unambiguous way) or a shadowy government conspiracy that has known about them for a long long time.