Counting binary words distance one from codewords

Question

If you have a [15,11] hamming code, how would you count the number of binary words that are distance 1 from codewords?

I know this code will have 2048 codewords, and there are 32768 binary words of length 15.

Answer 1

Hint 1: imagine $x$ is one of the 2048 codewords. How many words there are that are at distance 1 from that $x$?

Hint 2: Suppose $z$ is at distance 1 from $x$. Is it possible that $z$ is another codeword? Is is possible that $z$ is at distance 1 from another codeword?