WITHOUT land - just the house, 120 sqm, turnkey, without basement, without garage/carport, without controlled residential ventilation, without much frills --> not possible under €280,000 in my opinion.
--> Then there are all the additional construction costs like excavation, structural verification, permit costs/mortgage and so on... add another €50,000 on top of that, then you’re at €330,000.
Plus kitchen/certain fittings etc. - then you’re quickly at €350,000.
Then your land at €60,000 --> €410,000
Then also factor in the exterior work and buffer and you can reckon with a volume of around €430,000-450,000 MINIMUM.
These are prices for the BaWü area --> no idea how much prices vary in your region, you can just roughly deduct another 5-10% max, as BaWü is very expensive.