is {ww^Rw | w in {0,1}*} context free?

I say yes...
I can think of a PDA that accepts this language as the following:
Put all the symbols in w onto the stack, non-deterministically check to see if we have the reverse string by popping them off the stack.
If we reach an empty stack state then check the rest of the string to
see if it is in w.
Am I correct?
.

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