How do I implement a sequence generator using a universal shift register?
Consider the following representation of the sequence:

      0000
     1000
      0001
       0011
        0110
         1101
        1110
       1111


This should help you visualize how the sequence could be generated through a sequence of left/right shifts.

For each state, write out the previous state, and the required shift direction and shift-in value. These will be the inputs and outputs for your control circuitry. From that, you should be able to generate a Karnaugh map and the required logic.

(Every state transition is a left or right shift -- S1,S0 will always be 01 or 10. You do not need the parallel load mode for this circuit.)