While your options are probably limited since a lot of lenders have added minimum credit score requirements to their FHA guidelines, you should check around.
Just be aware that just because a lender will do a mortgage for a borrower with a 604 score doesnt mean they will do YOUR mortgage with a 604. It's not so much the score itself but the information behind the score.
This is because FHA underwriting guidelines use something called a "Total Scorecard" to evaluate an applicant's credit worthiness. Several of your qualifications - income, job length and stability, down payment, reserves, savings pattersn,previous housing payment history, and credit scores and history - are all analyzed and if you have multiple areas of weakness (called 'risk layers') then your loan may be denied.
So in other words, a teacher with a 604 credit score because whe had some small medical collections, but who has been in the same job for 5 years, never missed a rent payment, and managed to scrimp and save up money for the down payment is going to be more likely to get approved than someone new to their job who never paid much mind to managing their credit and who has to get a gift from mom and dad to find a down payment.
Hope this helps.