Something that might be worth looking into is the specifics that artists have to look into depending on the game engine.
Artists often have to work within considerable constraints (limited palettes for pixel art, specific 3D filetypes or map design with culling and portal rendering).
Some artists write the shaders for example. Texture artists create things like normal maps, bump maps or dirt maps.
Depending on where you see your role you might want to take a look at some 3D software like Blender or 3D Studio Max.
Blender might be nice because it is relatively easy to follow Blender development which gives a lot of insight into how programming and art come together.
Posts like this are pretty informative: http://mango.blender.org/artwork/shading-tests-dirtmaps/
You can also take a look at their feature lists (and the feature lists of 3D engines) and look deeper into the topics that come up during the research.
I fear that you will find that it makes a lot of sense to specialize more than you probably want to.
If you still want to get into programming / coding after researching some more you can try a very basic program that uses art assets which you create (starting from basic OpenGL or DirectX tutorials ... if you use something more sophisticated like Unity there will be a lot going on under the hood that you don't understand).
That should give you a pretty good idea of how those things play together.
The developer journals are also something you might want to look at from time to time.