Daniel's remarks about the history made me curious, so I checked my email, too. Things happened fast.

He visited Caltech April 19-30, 2000. During that visit we worked out properties of the codes, and had the idea to use them to prove security of QKD with squeezed states. https://twitter.com/preskill/status/1329873032626638848

On April 30, I wrote in an email about doing all Clifford operations with linear optics, including squeezing. Daniel replied, "I sort of knew that." His talk about the codes at Microsoft, attended by Freedman, Kitaev, and Shor, was the next day, May 1.

His report about that talk, emailed on May 2, indicates that by then I had already had a discussion with Hideo Mabuchi about how to prepare the GKP states by doing a measurement of q modulo alpha by means of coupling the data oscillator to an ancilla oscillator.

A gave a 30-minute talk at the SQuInT meeting in Albuquerque on May 19, 2000 called "Encoding a qudit in an oscillator." I still have the slides.
http://www.theory.caltech.edu/~preskill/talks/squint00.pdf

As the slides indicate, by that time Alexei had joined us. The talk notes that we can build codes in higher-dimensional phase space, that error rates can be small for finitely-squeezed codewords, and that we can prepare a magic state by measuring photon number mod 4.

I think Alexei had not yet suggested the cubic phase state at that point. It is noted that the magic state can be purified (Alexei's idea) without explanation. There is also a brief discussion of the QKD protocol, and its proof of security.

I'm not going to the office these days, so don't have access to my dated notebooks, just emails and talk slides. The paper was posted on the arXiv on August 8, 2000. The title changed (qudit --> qubit) later because Phys. Rev. A would not allow the work "qudit" in the title.

the word "qudit"