You could use "velký" it's informal and grammatically incorrect but common in speaked language.

Velkí is totally wrong, "velcí" is the correct word. And you use this only with plurar and "životné" masculine words. Because masculine nouns split into "životné" and "neživotné". Usually (but not always) living things are "životné". E.g.: muž (a man) is "životné", therefore velcí muži (big men).

Because such a word form does not exist. After k you always have ý, never í. Also, velký hrady is Common Czech, not Standard Czech, standard is velké.