You'll have to purchase the largest version of the pic. Even then, you will also have to scale the pic up depending on the layout. Get the file prep requirements from your print vendor. I scale grand format layouts at 25% final size @ 300ppi ( final res = 75ppi = plenty of res for your banner ). There are plug-ins like "BlowUp" you can use for enlarging pics.
Unfortunately the vendor is asking for at least 150dpi. I'm guessing the BlowUp plug-in will only make a slight impact?
That's 14 100 x 13 200 pixels. Of course no camera ever made is even close to delivering that - the current state of the art is the Phase One IQ 280 at 10320 x 7752 pixels.
So that means either a stitched image from several exposures, or upsampling. The latter is rather pointless IMO. An image from a good current DSLR, at roughly 5500 x 4500 pixels, should do fine. Exceptionally high resolution is good and well if you can deliver it, but you (and they) have to be realistic.
I've gotten requests like this on several occasions. Once I was asked for banner size at 300 ppi, weighing in at a neat 35 000 pixels or so long edge. In every case it turned out that they had no real concept of what resolution is, they just found some figures and multiplied by size.
Defintiley use the largest file size possible.I usually buy my images from either Dreamstime and iStock and there is typically an image in the 4000 X 5000 range at 300dpi, depending on the image and orientation. Images for banners are somewhat pixilated if you look up real close, but nobody is going to see it like that. By the way, here is a great letter visibiity guide for how high your lettering should be for viewing at various distances.