Are there more than 2 digits that occur infinitely often in the decimal expansion of √2\sqrt{2}?

The other day I got to thinking about the decimal expansion of $\sqrt{2}$, and I stumbled upon a somewhat embarrassing problem.

There cannot be only one digit that occurs infinitely often in the decimal expansion of $\sqrt{2}$, because otherwise it would be rational (e.g. $\sqrt{2} = 1.41421356237\ldots 11111111\ldots$ is not possible).

So there must be at least two digits that occur infinitely often, but are there more? Is it possible that e.g. $\sqrt{2} = 1.41421356237\ldots 12112111211112\ldots$?