How do I design a clocked synchronous state machine for a combinational lock?
Here is a partial version of the table you need to make. There is 64 rows in total. You determine the Q3*(Q3+) and the others by thinking what is the next state if I am in the current state and looking at X, Y.

Take for example line 2 : Current state 0000(RESET) and X=1, Y=0 this means the next state is 0001 (UNLOCK). Also Z is 0 when I am in state 0000.

You then get the output logic for Q0* by taking all the 1s in your column Q0*. For example for now I have (\ means "not") 

Q0*= \Q3\Q2\Q1\Q0X\Y + \Q3\Q2\Q1\Q0XY + \Q3\Q2\Q1Q0\X\Y + etc...

You can then most probably simplify this expression. You won't really be able to do Karnaugh tables because there is 4 states bit and 2 entries = 6 dimension. I suggest you use the cannonic method for the logic as I explained just before.

You can check here for more info :  https://en.wikipedia.org/wiki/Canonical_normal_form