I now know my battery is due for a replacement, without starting the car, it goes to 11.7v in 5 days.
It's probably my water pump failing, but could be related to the battery too : i found two threads on other forums of people getting the 2EE6 code and this problem because of a bad battery.
The limp mode didn't pop on the dashboard, nor in the DME codes (only 2EE6). I just felt it was like a limp mode (less power like turbo were disabled)
My car is 65000 miles (so that matches with a water pump life duration), and i don't know if the water pump has already been changed, i assume it's the first one.
I will update if it happens again and thank you for all answers
