Can motifs be found outside of phrases, like by itself? Or do you think that would actually make that "motif by itself" act like a phrase in it's own right?
Let's define both terms, as there seems to be a little confusion with what a motif and a phrase is.
A phrase is defined as:
A musical phrase is a unit of musical meter that has a complete musical sense of its own, built from figures, motifs, and cells and combining to form melodies, periods and larger sections; or the length in which a singer or instrumentalist can play in one breath.
A motif is defined as:
In music, a motif or motive is a short musical idea, a salient recurring figure, musical fragment or succession of notes that has some special importance in or is characteristic of a composition: "The motive is the smallest structural unit possessing thematic identity".
So a phrase can be thought of as a complete musical sentence, whereas a motif can be thought of more as an idea or theme that makes up that sentence.
Even if you do write just a motive as a complete musical sentence, by definition it is still a phrase, so no matter how you try to write your motif, it will still be a phrase or part of one.