Both are correct. A is often omitted before 'part' possibly because of the word apart (??I'm not sure really) and the confusion that might arise from this.
after analysing different examples with a part/part, one could reach several conclusions:
- using the article before 'part' gives more emphasis and renders the statement more precise, as in We've only finished a part of this project (=we've completed something we can clearly point at and assess). Cf We've only finished part of this pr