WorldCat.org identifies a few libraries that have the sheet music, described thus:

I GOT A CODE IN MY DOZE (sometimes punctuated: I GOT A "CODE" IN MY "DOZE")
Words and music by Arthur Fields, Fred Hall & Billy Rose
New York City: Santly Bros., ©1929

Furthermore, I have found that it was sung by Barbra Streisand in the 1975 musical film "Funny Lady" (the sequel to "Funny Girl") and is on the sound-track album. Assuming that film was historically accurate, it must have been in the repertoire of Fanny Brice as well, but I haven't found any confirmation of this.

The Online 78-rpm Discographical Project lists recordings by:
Duncan Sisters, 1930
Fred Hall & His Sugar Babies, 1929 (which you can hear at RedHotJazz.com)
Harry Reser's Syncopators (Tom Stacks vocal), 1929
Zelma O'Neal w/Al Goodman Orch, 1929

The Fred Hall version suggests a few improvements in the lyrics:

Pass that handkerchief....
Get a pail and soak my feet....
Bought myself galoshes, flannel union suit....

My hunch is, Gracie deliberately changed "union suit" to "undies too" because audiences in the UK were unfamiliar with the term "union suit." I'm not sure about the others; maybe I misheard them.