Do I have a chance at getting into Warwick?

I have recently started sixth form and I'm thinking about which university I would like to go to after my two years. So, I done awful at GCSE, I went to a very bad school so in comparison I done pretty well (Top 10). My results are as followed:

Maths: A*
English Literature: A
Religious Studies: A
Additional Science: A
History: B
English Language: B
Core Science: C
Spanish: C
Graphics: D
ICT: Merit

So, I really didn't put a lot of effort into my GCSE's, I was definitely too cocky throughout High School as I always expected to get straight A's up until Year 10. I only started revising in the dire moments (4 Weeks before the exams) and then i knew it was too late. I noticed how students from other schools done about 12 GCSE's which makes me really feel like I'm at a big disadvantage already. I am determined to get good AS and A2 results.

My options are as followed:

Maths
Further Maths
Economics
Computing

So my question is, if I get straight A's at AS, would I be able to get into Warwick or somewhere of equivalence?
I would be most likely applying for computer programming course, or maths.