Hmmm...being indoors means that you will be hearing more noise from other sources in your vicinity pretty easily. I don't think the G4000A would work all that well with coax fed antennas (most portables wouldn't, the new E1 from Eton probably being the only exception....) - but all is not lost.
We have a few possibilities on the antennas wiki (mentioned in the sticky at the top of this forum). These include the Carpet Loop (something I've been trying with my RX320 and seems to work pretty well), some of the links on the AMANDX website, and if you'd like to try a kit (would need some mods for portables, but would be a real possibility), the North Country active antenna. The mods for use with this antenna for portable use is detailed here...
Generally speaking the ones that would be most useful with a portable would be ones where the gain could be reduced. Actives usually work better - if at all, in some instances - with desktop or computer controlled receivers, not portables. Actives sometimes just have too much gain for a portable to handle without serious overloading issues.
There are active loop antennas; some of these are quite useful for portables, but are generally very expensive. If you're interested in that side, check the loops wiki page for some online reviews.
Don't be afraid to get out a soldering iron and build something. If it doesn't work, the only thing you're likely to damage is your wallet. 73s Mike