I'd appreciate info about the overnight ferries from Barcelona to Genoa. We are considering using the ferry in late May 2014.
You can check the website www.directferries.it to check your options for any destination with any company. Actually I think the Grandi Navi Veloci company (www.gnv.it) is the only company operating in that segment, therefore you might want to check their website directly. Journey time is a long 20 hours and it's not cheap. You may want to consider flying. Vueling flies from BCN to GOA (seasonally).