It is my understanding that if the word “foot” refers to the body part, its plural is “feet”, whereas for the unit of measurement the plural is usually “foot”. Usage may vary, though, and its probably not exactly what the OP is looking for since the two meanings of “foot” are not really homonyms, they’re the same word used with different meanings in different contexts.
A similar instance of this might be “monies” (financial resources, as in “Congress approved the monies to do whatever”) and “moneys” (currencies, as in “the different moneys used in Europe”). But I’m not a native speaker, so it might be that in both uses both plurals are acceptable.
I can’t think of any case in which the plural of the unit of measurement is “foot”; it’s always “feet”. (“How long is the pole?” “Six feet.”) Maybe you are thinking of when the term is used adjectivally, such as “a six-foot pole”, or (abbreviatedly) when giving one’s height. However, this is no different than with any other unit of measure, whether conventional or nonce: “a two-metre pole” (rather than *“a two-metres pole”) or “a seventy-apple crate” (rather than “a seventy-apples crate”).
“Goose” meaning a tailor’s implement has the plural “gooses”.
I learned this from a Ripley’s Believe it or Not entry. After I confirmed it in a dictionary, I wrote both answers on a test back in elementary school. I got docked a point by an unimaginative teacher who had no interest in confirming my claims.
Indeed. Most of the examples given have been pairs of words that are very closely related, etymologically, and therefore not really homonyms. We’re looking for words that fall into two unusual categories - true homonyms, and irregular plurals - so I suspect there are very few such words.
Dwarfs = Little people
Dwarves = fantasy creatures with beards who like beer and carry axes
Not the best example I know. I’ll bet you can game the system if you use loanwords from languages like Japanese, where you are technically not supposed to change the plural (ninja>ninja), or like Italian, where the “true” plural can be intermittently used, like lasagna>lasagne, or the plural is used for singular, panino>panini. I wish I could think of homonyms using those examples, the best right now is English pan>pans, and Japanese pan>pan (bread, itself a Portuguese loanword).