2010 Cali - Water shaking noice

Water sloshing noise? Are you sure it's not the window washer fluid?

 

You may have a blocked sill/rocker drain. A friend of mine once owned a Rover that did this, it turned out the sills were holding gallons of water. The stereophonic water sloshing sounds were interesting while driving.
Not sure why on yours it would only occur after 10km though, it might collect while sitting and first need some dispersion for it to become noticeable.
Do also a test with a full fuel tank.

 

Are you running the air conditioning when this is happening? Possibly a clogged drain with condensation building up and that's why the delay in occurrence.

 

Maybe you can get a buddy to hang off that side of your car and listen while you drive after 10 km? Oh wait, that would totally mess up the handling of your car. My bad, forget it.

Seriously though, here's another possibility - I wonder if the "water" may actually be inside the door.

If you live in a rainy area, water may have accumulated inside the door if the drain holes along the bottom become plugged for some reason. When you drive that first 10 km the braking forces that you apply may by momentum thrust the water into a forward space inside the door when the car comes to a stop. The water then sloshes around until it leaks out or back into the rear of the door.

Here's a diagram from Ricambi America website showing the door panels. Notice items 18 and 19 refer to rear and front water shields.

 

There are hydraulic lines which run under the drivers area.
They do produce some sound. Ferrari made a couple of modifications to both the software and the lines themselves to minimize the sound.

I would bring the car into your service center and ask them to look into it.

Yes it may cost some money, but then it may solve your problems and then you can get back to enjoying your car to the fullest!