Modularize is pretty much the accepted term here. Any other software engineer will understand what you're saying when you use it.
Im not a massive fan of it either though, so I've experimented with alternatives over the years.
The most intuitively grasped so far has been partition, as in "Yesterday I partitioned the project into 3 different libraries."
There's the obvious and simple split, as in "I split the project up", but it's somehow unsatisfying. Largely, I think, because it lacks emphasis.
If the partitioning was due to messy code, which likely means there were also other things wrong, then I use the broader term rationalized. "I rationalized the code into a set of modules with clearer interfaces" That doesn't explicitly mean partition, but practically speaking that's what rationalizing a code base usually entails.
I've tried decompose, but in speech it doesn't ring quite right. Probably because decompose is also used to refer to the process of animate organic matter breaking down after it dies.
For similar reasons break, as in "I broke the code into smaller modules" feels horribly wrong. I didn't break the code!
There are two cousins that I've heard used, and I'm not entirely opposed to them: box and package. "I boxed up the submission code into its own module" or "I packaged that chunk into its own module". Interestingly, graphic layout language uses the word 'box' for callouts and sidebars, describing them as having been "boxed out". As a result I've also heard people say, "I boxed out that chunk of code." Obviously to a software engineer, the using package as a verb here is more familiar, as the noun package as in "code package" is used as a synonym for module.
Finally, I've also used isolated, specifically when referring to a chunk of code that needed to be kept away from the rest of the code base. "For security reasons, I isolated the password mangling code into its own module", or "This stuff is mostly throw away work, so I isolated it into its own module."