Random misfire after 10 hours stop

[lordthomas]

Hello!
I have been suffering from one (or more?) faults for more than a year and the mechanics can only guess (not with much luck ). 2016 1.4, 120hp, 100k. km, (940B7000) produces the following phenomenon:
1. After a long standstill (about half a day), if I start the engine and it runs for 5-6 sec, the check engine light stutters, the car shakes and the check engine light flashes for 10-20 sec. The issue comes when starting for the first time after 10-12 standstill (If I stop the engine after the first start and start it again, there is no issue). According to diagnostics the following error codes has the car: P0300-301,302,303,304 and P2097. (Random misfire, cylinder 1-2-3-4 misfire, upstream lambda probe). The check engine blinks for about 5-8 seconds, then the error disappears and the engine runs smoothly.
2. Sometimes after the first start, the check engine lights up continuously, it is also present as a residual error. I have already replaced 3 times the spark plugs (all 4 of course) and lambda sensor. The continuous Check engine sometimes only comes back after 2-3 months, but it's always the same error code.

Also the end of the exhaust pipe is very sooty.

So far:

1. The lambda sensor has been replaced with a new one.
2. The spark plugs have been replaced with new ones 3 times.
3. MAP sensor has been replaced with a used one and after that with a new one.
4. Battery checked
5. Fuel sensors and fuel pressure checked.
6. Engine compression checked
7. Fuel injection checked

All values correspond to the factory specification. The car were in several italian car specific service in Hungary but they have not clue what cause the issue.

I would be grateful if you have any idea what cause these issues.

Best regards,
Tamas