If Heller held that it was a right to carry it would have forced DC to implement some kind CCW or Carry law which it didn't.
The holding in Heller was:
Quote:
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In sum, we hold that the District's ban on handgun possession in the home violates the Second Amendment, as does its prohibition against rendering any lawful firearm in the home operable for the purpose of immediate self-defense ... We affirm the judgment of the Court of Appeals.
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Such a holding does not make it a right to carry. Much of the discussion in Heller hints at a right to carry but that was not the holding in the case.