How do you get an object of 44 Earth masses with the average density of styrofoam? The obvious starting point I guess is a core of very light elements, and a r

How do you get an object of 44 Earth masses with the average density of styrofoam? The obvious starting point I guess is a core of very light elements, and a really really extended atmosphere. But an atmosphere thins out exponentially, more steeply the higher the gravity. So for an atmosphere to help much, those 40ish Earth masses of hypothesized core need to be spread out a whole lot already. It seems like a difficult planetary engineering problem -- spin it up almost to bursting? So taking that to be too silly, the core must be only a small fraction of the mass: a big gas cloud with a nugget in the center. I'm not sure that could work, but it's what I'd try to work out next.