The OED defines ungrammatical as

1. a. Not in accordance with the rules of grammar.

(It also says that the word "gibberish" is "often applied contemptuously to blundering or ungrammatical language." Searchable dictionaries are wonderful, aren't they?)

So yes, MG, it's a real word.

My own handle being "nerd" is not unrelated to to its rhyming with "word." One of the nicknames I have been saddled with in my life is "word nerd."

I have also been called other kinds of nerd, however...