Faith, we literally don’t know the answer to your question. God has not told us, and it’s the sort of information we’d have to get from Him.
We can infer that something like space and perhaps something like time exist, because there are bodies there (and will eventually be many more). On the other hand, these are bodies that can appear and disappear at will (as Jesus did after the Resurrection), so how their “space” works is mysterious to us.
We generally don’t think any longer that Heaven is literally in the sky or in space, because we can visit those places now and they are just normal, obeying the same laws that we do on Earth (which turns out to be one planet out of many orbiting one star out of many, rather than the center of the universe with Heaven above and Hell below).
“In a higher dimension” is a decent analogy, at least; I’ve used the notion to illustrate how God could possibly exist “outside” of time and space as we know them, using similar examples to those of Edwin Abbott Abbott’s Flatland: A Romance of Many Dimensions. However, I suspect that any higher dimensions we discover will turn out to be part of the created universe just like space and time, and so even that is probably not a good bet for where Heaven “actually” is.