If Utah chooses to appeal this latest ruling (which the judge has put on hold for the state to consider its options), it will be up to the Supreme Court to decide if it wants to hear it.
In the majority decision, Judge Carlos Lucero writes, "We hold that the Fourteenth Amendment protects the fundamental right to marry, establish a family, raise children, and enjoy the full protection of a state’s marital laws. A state may not deny the issuance of a marriage license to two persons, or refuse to recognize their marriage, based solely upon the sex of the persons in the marriage union." Read the decision here.
In the dissent, Judge Paul J. Kelly said the court was overstepping its authority: We should resist the temptation to become philosopher-kings, imposing our views under the guise of the Fourteenth Amendment."
Assuming Utah continues its appeal, the Supreme Court would have to decide to take the case up and consider whether setting a legal precedent that gay marriage recognition is or is not a right. If they decline to take up the case, technically they are avoiding the precedent, but given that federal judges have been striking down gay marriage bans wherever they’ve been challenged (less than an hour before this announcement, a judge struck down Indiana’s ban, and the state has already begun handing out marriage licenses), gay marriage recognition is likely to become the law of the land anyway.
UPDATE: Utah's attorney general has said he will be asking the Supreme Court to take the case.