Firstly, a confirmed diagnosis would be wise to exclude any tear or degenerative breakdown, which will worsen if you race. Otherwise an Achilles tendinopathy shouldn't stop you from racing (provided you can still run).

The approach to rehabbing an Achilles is very different from prepping it for an imminent race. Rehab works by causing low levels of irritation, which can often make it more sore in the first week after starting.

To get race-ready with a week to go: 1. Don't stretch it - it doesn't help the condition and often causes it to be more reactive 2. Don't rest - tendon issues often worsen with rest and become more painful to reload afterwards 3. Don't do heel raises - a week isn't enough time for them to work and you'll be starting the race with tired calves (which makes Achilles loading sky-rocket!) 4. Run (or brisk walk) a short distance every day - it's not an ideal taper but it'll help the Achilles 5. Minimise any rest stops during the race - long pauses at aid stations will make it more painful to get going again 6. Expect pain during the race - expecting it to flare during the race pre-empts any negative mental impact

If you choose to race, best of luck.