You can try contacting DreamHost and explaining the situation, they may, or may not, be able to apply a promo-code for you retrospectively.
If you signed-up using a credit-card, you could always take advantage of the 97 day money back guarantee and then sign-up again. Although, you will not be refunded for the 'free' domain registration and I think you would need to use a different credit-card for the second purchase.
Overall, unless DreamHost can retrospectively apply a promo-code for you, I don't think anything else is really worth the effort. After all, DreamHost is exceptional value, even at the full price
Edit: After further investigation, I don't think you have much chance of DreamHost applying a promo-code for you 'after the fact'. The sign-up page clearly states "You may not change/submit a promo code or referrer after you've finished signing up."
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