Long before 1968, when the "American Standard Code for Information Interchange" was created and abbreviated to ascii, and the more recent development of unicode, those words were in the dictionary.
Ascii was the plural of Latin "ascius", from Greek "askios", meaning "shadowless", from "skia" meaning "shadow". The word referred to the inhabitants of the tropics, where at some time of the year, the sun is directly overhead at noon, so that people don't cast shadows (except directly below them). A more anglicized form was ``ascians''.
(Incidentally, the word "skia" is also half of the root of "squirrel". The Greeks called the animal "skiouros", "shadow-tail"; i.e., animal which uses its tail as a shade; which was taken into Latin as "sciurus", with a variant "scurius". Vulgar Latin used the diminutive "scuriolus" which became Old French "esquireul", from which the English word comes.)
Unicode is more recent. It is described in the Oxford English Dictionary (2nd ed.) as "a telegraphic code in which one word or set of letters represents a sentence or phrase; a telegram or message in this". These words were apparently listed in a booklet "Unicode: The Universal Telegraphic Phrase-Book", for which they have an 1886 reference. Unicode was one of many such telegraphic codes.