Set up your computer with your personal credentials first an then activate and install the free one year Office (watch for, and turn of, auto renew during activation). You need to do this prior to a clean Windows install, before logging into your work account, or you might lose the free copy. Next, uninstall Office to save space - don't worry, for the next 12 months you can reinstall here or on another Win or Mac computer plus on a tablet.
Next, set up another user with Admin credentials - this would be your work account. Since you have limited space on this machine, from your work account log in, delete your personal account in Settings=>User.
Now you've saved your free Office in case you want it in the future, but your machine now has your work account and Office from work downloaded.
Since there is no coupon code - the free offer is hard-coded to the laptop - you have to use this work around to activate and save your free Office.
Or you can just set it up with work credentials at the outset and download your work version, but you risk losing the free offer.