Honestly, we already have trouble just imagining the capacity of 1, 2 and 3 dimensional spaces to be subdivided infinitely. We can't even address (as in give names to) the majority of non-rational numbers very well, and the majority of that line-space remains effectively unmapped mentally on an infinitesimal scale.

4th dimensionality gives each point in an infinite and infinitely divisible 3d matrix an infinite degree of variation, each point now contains a whole line. 5th dimensionality gives each point 2 degrees of that variation, each point containing a plane. And, 6th dimensionality gives each point in an infinitely dividable matrix its own whole 3D vector space. Past 6th gets even more tricky as we're forced to stack metaphors, infinite lines in infinite spaces in space for 7th and so on.

Beyond that stacking of metaphors, I don't think we can really picture it, if you mean visualizing in the more traditional sense wherein you could attempt to commit a scene to canvas or something.