Absolutely not.
First of all, Colorado does not have a statute for the emancipation of a minor. A minor who, with parental permission, has been successfully living on their own and managing his or her own financial affairs might possibly be considered emancipated by the state, but your state does not have a statute by which you can go to court and become emancipated.
Secondly, even in those states that do have such statutes, only two will even consider emancipating a 15 year old, and in those two states to be emancipated that young you'd better be either a nationally recognized sports figure or a successful child actor or musician. Even that won't always do it - Lee Ann Rimes was turned down for emancipation.
Third, there is not a judge in the US who will emancipate a minor so that she can go live with her boyfriend. It simply will not happen.
Fourth, in those states that do have a statute for emancipation, emancipation requires that you be capable of SELF-support. Not that you go live with someone else so that they can support you. "I'll get a job when I'm emancipated" won't cut it. Unless you ALREADY have the job AND can provide a budget of "I earn xxx.xx per week of which this much goes to rent, this much to utilities, this much to food, this much to transportation, etc." you're dead before you start.
Finally, emancipation is not and never was intended to be a means for a minor to leave home. It was and is intended to provide legal protections to those minors who, through no fault of their own, find themselves living alone.
Emancipation is NEVER granted on the basis of how bad you have it at home. In the very, very rare cases that it IS granted, it is based on your successful record of ALREADY being on your own.
If you are being abused, your recourse is to call CPS. Emancipation is not, repeat, NOT an option.