I agree with Steve. Contact your local lumber yard that sells beams and trusses and engineered beams, etc. They can size it for you. Tell them that it is supporting another floor. The spans are different for different types of lumber and beams. You may want to consider a steel beam also.
I've seen triple 2by12's used in a similar size situation but yours is supporting another story also. According to tables I have, 13'6' may be stretching it for triple 2by12s. Before going to quadruple 2by12s, I'd look to engineered beams or steel. A lumber yard that carries beams and builds trusses can set you up or get an architect or engineer to do it. I don't know if the home cheapos are set up to do that or not.