Hi Shadowless,
Welcome to babybmw. I suspect that someone has had problems before you and relocated the module. I did this with mine and velcro-fixed it higher up just underneath the little shelf with the rear speaker in it.
If you haven't already, remove the internal panel on the RHS of the boot and you should find it nearby. Also worth checking underneath the carpet panel at the bottom of the boot in case it's been relocated to one of the recesses under there - perhaps just in front of the battery?

 

Hello, thank you for your response, I looked around the lower right corner as shown in the photo, I can't even see the harness, I also looked next to the battery and completely removed the trunk carpet

 

Unless it's an aftermarket PDC ?
You could try following the cables that run through the body from the sensors.

 

Hello, no it's not an aftermarket PDC
Yes I could follow the wiring of the sensors wire by wire but I think it would be a hassle and I would have to remove the rear bumper

 

It's not wire by wire. It'll be a harness taped together and the only ones going through the bodywork to the bumper. Not rocket science.

 

I continued my search by examining the left side. I removed the trim and found a small gray box from Valeo behind the rear light. Following the wiring, I identified the cable that leads to the parking assistance sensors. Thus, I believe I have located the PDC unit, but at first glance, it is not the standard white module; this one is gray and has the Valeo reference 10R-03 2055. Therefore, I am unsure if it is an original BMW unit or rather an aftermarket solution installed by the previous owner. The issue is that the white module with the BMW OEM reference is readily available on eBay, whereas I do not know where to find the Valeo one.

 

So I was correct regarding aftermarket and also following the harness.
It might be worth sending the module away for testing and repair. I'm sure a Google search will find someone who'll look at it.