It was a twin too, though an old one. Will be interesting to hear about the cause. Sad story, RIP.
More telling is the report of heavy fog. I'm surprised they aircraft was cleared for takeoff under those conditions. As a VFR pilot, I recall the minimum acceptable being around 3,000 ft AGL. "Scud running" i.e. dodging clouds was considered poor practice. The FAA regularly sent a newsletter detailing accidents and their causes.
Cause will be pilot error (aka stupidity)