And in the context of animals, it's particularly unusual to use the adjective 'great' by itself, without it being part of the breed name. 'Great big' maybe, but rarely just 'great'. If you saw a large bulldog, it would sound strange to call it a 'great bulldog' instead of a 'great big bulldog' or other adjective.
This being said, because of their most prominent colour, we can talk about "gray great white sharks", and get the colour in on both sides :)
He's a great bulldog.
If someone says "I have a great bulldog", it generally means a bulldog that's excellent in some way. If someone says "I have a great brown bulldog", it's more likely that they're now using 'great' to talk about size.
using BNF, you might say something like [noun] := [adjective] [noun]
But this is not what the original post is getting at. For some reason, if you want to describe a house as being big and red, you must(1) use "big red house", and not "red big house".
1) Whereby "must" I actually mean in the vast majority of cases. There are always twisted counter examples, like: "Aaron: Wow, look at all of those big houses - aren't they so much prettier than the little houses! Betty: Well, mostly, but if you look at the red big house, it's actually much uglier than even the little houses"
This counter example (mostly) works because Aaron first identifies "big houses" as being a noun group, so Betty can adjust the noun group with the red adjective.
I mean, if you were reading a book, a good author might go into detail about how "great dragons" or "green dragons" are a different species from "dragons" before using both in long chains of adjectives. Maybe it is left ambiguous on purpose, just to exercise the reader's imagination.
So yes, it does imply something, but only because "green great" is considered wrong.