You could use a MFJ Loop tuner such as the MFJ-933 or MFJ-935 near a window. I have one and it is simply amazing for what it is. You just supply a piece of 1/4" copper tubing or #10 wire.
I think a long piece of wide copper strap -- perhaps 5 cm to 10 cm in width -- would also work well, though you need use gloves and to be careful to avoid cutting yourself on the razor-sharp edges of the copper strap. A copper strap has the beneficial combination of high conductivity and physical flexibility so you can dismantle it and roll it up easily when not in use.
The best loop size is the largest possible, while remaining below self-resonance. This corresponds to a conductor length of about a quarter-wavelength, and the conductor should be stretched out to form a large, single loop. But if your space is limited, you can also try winding the conductor into a two-turn or multi-turn loop.
For 20 meters, a quarter-wavelength is about 5.35 meters, which corresponds to a circular loop of about 1.7 meters diameter or a square loop of 1.3 meters per side, which is a fairly small size and should be quite efficient. I did a quick 4nec2 simulation of a 1.3-meter square loop, 1.45 meters above moderate ground, with round copper conductor of 2 cm diameter (corresponding to about a 10 cm-wide copper strap; see equation 16 at
http://web.archive.org/web/20000506045342/http://fermi.la.asu.edu/w9cf/articles/conform/index.html, the accuracy of which I have verified via Finite-Element Method simulations), and an added capacitor loss of 200 milliohms (corresponding to a capacitor Q of about 2400 at 14 MHz when resonated with 24 pF capacitance).

At 15 degrees above the horizon, the gain is only 3.81 dB below that of an isotropic radiator. That's not bad for an antenna of this size, so close to the ground.
As already mentioned, the biggest problem will probably be RFI (both on transmit and receive) inside the apartment building. So you might want to consider portable operation from a park.