There are no less than eight versions of this washing machine, which one do you have?
However fault code E03 is indeed a drain timeout or a failure to drain. This could mean a faulty drain pump as it could cut out after running for too long or, it could be a blockage which, given what you've said is more likely. In a lot of modern machines that use a pressure sensor (that's the sensor detecting the error) they can be fooled into thinking they've not drained when they actually have done.
This isn't the fault of the machine, it's got more to do with the user.
What can happen and, often does, is that low cost detergents are used or, too much detergent or, quick wash programs with a normal dose of detergent or any combination thereof that leads to over foaming. This foam gets stuck in the pressure sensor hose and stays there holding the sensor "open" and in turn making the machine think it hasn't drained when, it really has.
After a while the foam dissipates and the machine goes back to working normally as it should.
Bear the above in mind if you can't find anything actually faulty as it's very common these days to get that issue.
Your E16 error is a problem with the heater or heating circuit, it's reporting an error with the heater basically.