The copper colour will almost certainly be a tinted clear coat rather than paint, so that might be why you’re struggling to get a paint code. The tint will be added to the clear coat (also known as a barrier coat) and then be applied to the face of the wheel after it‘s been machined / diamond cut on a CNC lathe.
Tinted clear coats on diamond cut alloys are known as special effects, and the place at the link below have a picture on their website of a diamond cut alloy that they‘ve refurbished with a special effect copper tinted clear coat. So there’s a good chance they‘d be able to refurbish your damaged alloy back to OEM factory standard;
Diamond Cut Alloy Refurbishing | Alloy Care Centre | Experts in alloy wheel refurb and repair across Hampshire, Surrey and West Sussex | Call 01428 751 899
www.alloycarecentre.co.uk