All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Gathering to recite the Quran and to remember Allah are among the recommended acts of worship, as in the Hadith narrated by Abu Hurairah in which the Prophet said, “There is no group of people that assemble in one of the Houses of Allah to recite the Book of Allah, learning and teaching it, except that tranquility will descend upon them, mercy will engulf them, angels will surround them and Allah will make mention of them to those (the angels) in His proximity.” [Muslim]
There is no doubt that one of the greatest blessings that a person hopes to befall him is Allah's remembrance of him, the descent of tranquility upon him, being engulfed by mercy, and the angels' surround him.
In addition, the fact that this meeting is in the house, this is permissible, although if it is in the mosque is better due to the place being so special, and for what was mentioned in the Hadith: “There is no group of people that assemble in one of the Houses of Allah...”
Accordingly, such a meeting is good if it is not taken as a regular act of Sunnah, such as allocating a specific day for this meeting intended for a virtue that is not mentioned, or reading a specific Surah, with a specific number because of believing in a virtue that is not mentioned in the Sharee’ah.
Forewarns against reading the Quran together with one voice, as this is something that is not proven in the Sharee’ah to be permissible. Rather, what is permissible is that one reads and the rest listen, then another reads, [and others listen] and so on.
Allah knows best.