At the very least the sentence needs a comma after Hopefully.
The use of the word "Hopefully" to mean "it is hoped that" is much debated, with the old guard staunchly against it. However, all languages evolve and with general usage the word now is more readily accepted.
The word hopefully seems like a common word with a well-known meaning. But because it's used improperly so often, its use can be highly annoying to many. Hopefully is an adverb. It's not a verb, as it is most commonly used. The use of hopefully as a verb in its own right usually comes from a mistaken belief about the meaning of the word. Using the word hopefully as a substitute for the phrase "I hope" or "it is hoped" is the most common, but incorrect, usage.
The Correct Usage -- Using the word correctly as an adverb means to substitute it instead for the phrase "full of hope" or "in a hopeful manner." When unsure whether the word is being used correctly, simply use one of those phrases instead and see whether the sentence still makes sense. There are far fewer times to use the word correctly than there are to use it incorrectly, which has made many grammar sticklers angry about the word being used at all.
Except for the missing comma, conservative grammarians would say it is grammatically correct if it means we're hoping to find someone or something there when we arrive.
The American Heritage Dictionary argues hopelessly :-) that there is no good reason why it is not an accepted way of saying, "We hope to be home by twelve."
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