I believe what you need is called a "sewage ejector" (images:
Ejector Images) - it is a sealed-with-bolts (*) sump and pump installation that then can send your sewage just about anywhere properly without smell, backups, etc.
Simply installing, say, a sump and pump that is meant for something else and sending the liquid UP somewhere pretty much guarantees some quantity of it will fall back down.
Doing a quickie Google Search for "sewage ejector noise" returns plenty of hits, some strongly suggesting the sound is minimal for a properly working system:
Sewage Ejector Noise
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(*) A "regular" sump and pump just has a simple drop-in-place cover that isn't meant to keep anything in the sump - it's just (flimsily) covered to keep things from falling in