You're right, from the specs click here. it does have a PCI-E slot.
There are 3 models in the GX280 range click here. Which one do you have exactly ? You mention 'minitower', but is it the same as the one they also refer to as 'Small Mini-Tower' in the above link?
If it is indeed the 'Small Mini-Tower', then the best card you could install is a ATI HD4670, e.g. click here. Open the case & have a look at the PSU rating (in watts) & also the physical space available next to the 16x PCI-E slot. These graphics cards can be quite broad due to the large cooler & occupy 1-2 adjacent slots. G