I'd like to clarify that you are referring to spatial dimensions here. The word dimensions refers to a lot of other things for, for instance "my different dimensions of thought" or "dimensions of knowledge and equality". It can be used to describe various aspects or similar things in co-existance with the same thing only it being quite abstract at the same time.
Imagine though that as string theorists posit 11-dimensions, perhaps there could be multiple time dimensions and we have just to this day conceived of time in an incorrect manner.
Look at this, this is exactly the sort of visuals that I see on DMT and it is a mathematical rendering of a special type of manifold that is described in certain branches of theoretical physics, super-string theory and mathematics such as algebraic geometry:
[youtube][MEDIA=youtube]b-ja3hQ38wc[/MEDIA]
The problem with your hypothesis is that language does not exist in a concrete sense in the way that say a chair exists in the living room. Language is a tool that uses symbols to tie identification from words to objects or locations or feelings or concepts.
What you can say though is that objects in the physical world are a language in themselves and when we talk about them with language we create a new language or dimension about an already existing language. But then you would have to prove that objects in the world exist as an objective language which would be tough because you need a subjective individual to create meaning supposedly or allegedly according to us.
However, if you could imagine the mind to be something else than just a subjective experience existing in the brain then perhaps you could say language is a dimension although it would be hard to talk about that without reading a lot of information about alternative theories on the philosophy of mind.
In fact, language enables us to process information at enormous speeds compared to other primates who take quite some time just process the fact that they have a red ball in front of them. It is in a way a dimension of understanding or a dimension of existing even but to say it is a physical dimension in itself is getting quite absurd and it is at that time when you should know to put the joint away 