My drain is from a double bowl sink . The drain comes from each side to the center. They join into a T which is connected to a trap and the drain then goes into the wall. There is no real drop in the pipes, and no place to put in a drop pipe with the neck for the dishwasher drain to enter into. Do I need to install a new drain that goes through the floor and then connect into the drain in the basement?

My drain is from a double bowl sink . The drain comes from each side to the center. They join into a T which is connected to a trap and the drain then goes into the wall. There is no real drop in the pipes, and no place to put in a drop pipe with the neck for the dishwasher drain to enter into. Do I need to install a new drain that goes through the floor and then connect into the drain in the basement? To go through the floor woukd be building a "S" trap which is outlawed. How much space is there between the center outlet continuous waste tee and the trap? Could a branch tailpiece ,(see image) be cut back and installed? If not a trap will have to be cut in and the discharge hose connected to it after first running a high loop for a air gap. Good luck, tom