It is not correct. The reason why it is not correct is not simple.
We use the 's form (the "genitive" or "possessive") to indicate possession or ownership Fred's money
and various other relationships that are similar to possession - extensions to the idea of possession Fred's cat
the chair's leg
we also use it with nouns that themselves specify a particular type of relationship Fred's wife
the firm's employees
the employee's firm
and a few other relationships, such as the relationship between an action and the person who performs the action Fred's singing.
There is more here: Possessive - Wikipedia
The relationship between grammar and the quiz is not generally felt to be similar to possession.
We would probably say A grammar quiz using the "noun modifier" grammar. I think that noun modifiers can be used in respect of all kinds of relationships; but this does not mean that they can be used in all circumstances!