You have three options.
1. Quit, this would appease your mother but not you, this is probably the worst option.
2. Don't get caught. Seriously this is not that hard just don't be stupid, you should have been on your shit after you got caught the first time. Don't leave weed lying around, don't let dealers deliver to your house, don't talk about weed around your house when your mom is home, take precautions regarding smell and bloodshot eyes. She obviously knows nothing about weed so this option should not be that hard. This option is OK but not ideal.
3. Educate her about marijuana and its effects on the human body. Most people who think weed is bad know nothing about it. If she understands marijuana she may be accepting of your using it. This is the best option, however, it is also the most difficult option. No offense but your mom sounds like an ignorant Bible thumper, convincing her weed is not all that bad will be difficult.
I was caught smoking weed when I was about your age, my mother is a staunch Catholic and had the same reaction yours did. I took option 2, it was the easiest and least confrontational. I did, however, slowly educate her regarding marijuana (option 3). Eventually, and I'm talking years later, she became tolerant of my smoking, so long as I remained discrete in my use and didn't smoke inside. Ironically I hardly smoke at all anymore.