Is JavaScript a homoiconic language?
Given your definition, the answer is "no". JavaScript syntax is not a subset of JavaScript's literal syntax. The fact that a value a literal represents can be produced by evaluating the literal is what makes a literal a literal and is true in any language. The only real difference is JavaScript has a richer literal syntax than many common programming languages, though this is certainly not a rare thing.

The answer is "no" for pretty much any reasonable definition that doesn't make practically every language "homoiconic".

My impression is there is not a clear consensus of what "homoiconic" means within the Lisp community. Part of that is it seems many Lispers are confused1 about "homoiconicity"2. I recommend this article which goes over the variety of possible definitions of "homoiconic" and the issues with each. As the title of that article is "Don't Say 'Homoiconic'", this suggests worrying about whether a language is "homoiconic" is not a great idea and you should be more specific about what it is you are care about.

If we use the definition referenced in the article, namely "having the internal and external representations be the same", then this definitely doesn't apply to JavaScript (to the extent that it even makes sense). It arguably doesn't apply to Lisp either, but there are various ways where Lisp gets closer to this. One small indicator is that Lisp's eval takes in Lisp lists while JavaScript's takes in strings. This separation holds for the actual Lisp implementation as well as parsing is viewed as conceptually outside of the implementation and so the implementation conceptually works upon Lisp lists. This has non-trivial consequences like being able to provide circular syntax and an abstract syntax graph in general. 

1 Frankly, understandably so as the explanations tend to be vague. There is also, at this point, a lot of misinformation.2

2 There are many definitions floating around that whatever "homoiconic" should mean if anything doesn't mean these things such as "supports higher-order functions".