Hatred of Eleven

We define an "Eleven Hater" as a number that is not a multiple of eleven, but becomes a multiple of $$11$$ when any one digit is removed.

For clarity, consider a 3 digit number $$\overline {abc}$$. if $$\overline {abc}$$ is an "Eleven Hater", then $$\overline {ab}, \overline{ac},$$ and $$\overline{bc}$$ should all be multiples of $$11$$. Note that the order of the digits are not to be altered.

How many 4-digit Eleven Haters are there?

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