There's nothing technically stopping us from simulating 4 spatial dimensions now. In fact, there are several games that utilize a 4th dimension in their gameplay. Here's 8 examples. The problem is that our brains evolved in 3 spatial dimensions and, even if we can conceive of, define the nature of, and to some degree even indirectly imagine a 4th spacial dimension, our brains are hardwired to think in 3 dimensions and our understanding of a 4th spatial dimension can only be in 3 dimensional terms. The software of our brains, and the hardware of our eyes are simply incapable of perceiving and processing a 4th spatial dimension as it truly is. It would always be filtered through the lens of 3 spatial dimensions, projected into a 3 dimensional form that we can understand.
For a good example of this limitation, we regularly show 3 dimensions in film, tv, animations, video games, etc. projected on 2 dimensional surfaces. We can interpret those 2 dimensional images into an understanding of the 3 dimensional spaces being projected, but A) we do not actually perceived them as 3d. We still only see height and width. Depth is imagined largely based on perceived scale and parallax oocclusion. and B) we are only able to see the 3 dimensional space in our minds because that is how our minds always perceive space. In order to make those 2 dimensional images seem actually 3 dimensional, we have to project different 2 dimensional images to each eye with precise focal lengths and angles to mimic our actual eyesight in 3 dimensional space. Only with that stereoscopic view do we actually see 3 dimensionality with actual depth. Now, with that understanding, that it takes 2 projections in 2d to trick our minds into seeing 3d, how would you trick our perception into seeing 4d? How to we make either our eyes or our brains see whatever the 4th dimensional direction is called? A 3rd eye? No, plenty of animals have more than 3 eyes or even compound eyes, and still only perceive 3d. We have to perceive a direction perpendicular to height, width, and depth that does not actually exist. How would you achieve that goal?
I don't think that is actually possible. I think, like those games in the link, even in a simulation we are stuck playing with the 4th dimension via its interaction with and projection onto 3 dimensions because our brains cannot truly process what a 4th spatial dimension would even be.