My spouse died in September 2012 does that qualify as an exemption for 2014 taxes / ObamaCare ?
A spouses death does qualify you for a hardship exemption. You do need to claim that exemption at HealthCare.Gov. There are limitations on exemptions (unfortunately this may include you not being eligible due to the timing gap for your specific situation):
Hardship exemptions are usually provided for the month before the hardship, the months of the hardship, and the month after the hardship. However, the Marketplace may provide the exemption for additional months after the hardship, including up to a full calendar year.
You'll need to provide:
Death certificate, death notice from newspaper, funeral service program, funeral expenses, coroner’s report, military notification of death, or other official notice of death.