Transistor with emitter resistor calculation
The simplified equations only work when you observe some basic assumptions. The most important being that the transistor is operating in it's linear region.

Leave out the transitor for a moment. How much current would you get through Rc if it was connected directly between the 20V supply and ground?

Then add in Re. You should end up with 20/(80 + 6.8) = 230 mA. This will be the maximum current that can possibly flow through the transistor. Given that there will be a small voltage drop across the transistor and errors from the resistor tolerance, that is very close to the measured value of 222mA.

Depending on what you are trying to achieve you may need to reduce the collector resistor or reduce the targeted collector current.