So,

After a removed things one-by-one I could define that something is wrong with the Piezo speaker I have.

Originally, the piezo was connected directly to the PIC's pin with a 1µF cap in parallel with the piezo.

Since I removed the piezo, the current is constant at 19mA.

In the PBP Compiler Manual, it says that you can connect a piezo directly to the PIC. But the sound is not good (like saturated).

How do I have to connect my piezo a correct way?