Yeah, you could represent the linguistic structures itself that way. I think it's correct to say, as you're doing, that language can also be seen as a 'space'. But when it comes to the whole relation between meaning and representation, i think we need a more complex system than one that can simply represent linguistic structures themselves.
Some linguists believe that the mind has it's own private language. A sort of 'brain-linux'. They think that without such a system, it could not relate meaning to linguistic structures. I don't know if that's true though.
But i think that if we would want to represent the 'mindspace', it would maybe be usefull to do the following:
So first we could maybe list all ways in wich 'meaning' can come into existence to the mind as we know it. You could call them a dimension if you like, but i guess it isn't realy relevant how exactly you'd define them. To represent meaning as it forms in the human mind, this list would be a list of all the known sensations: Touch, taste, smell, vision, sound, temperature, balance (the vestibular organ), probably sensations from within the body as well.
Then you'd have to represent information within each of these realms. Some of these realms require 4-dimensional representation (or more), but maybe some of them (bodily sensations like pulse, degree of wakefullness, bowell-activity, etc.) can be represented within a single dimension.
So then you'd have a picture of dimensions existing within dimensions (a location or set of locations, within a location or set of locations).
Any such Multi-dimensional structure could then represent a memory, a dream, a feeling, or a thought. Any point in this universe could be connected to a point in another universe. The linguistic universe. But as language is way less adequate then the mind itself is, a point within the linguistic universe could correspond with multiple points in the universe of the mind. Therefore a sentence could correspond with several meanings.
Or maybe i'm just rambling. Just had a few beers. In that case it's the booze talking. Not me. The booze just hacked my acount and typed this bullshit, then.