Marked 2-limits, or Cartesian quasi-limits introduced by Gray, give an alternative approach to Cat-weighted limits in 2-category theory. The equivalence between marked 2-limits and Cat-weighted limits was first established by Street, and we aim to give a new approach to this result using marked codescent objects of marked coherence data which we explain in this talk. We introduce the notion of enhanced marked 2-limits, which is a natural generalisation of marked 2-limits to the enhanced 2-categorical setting. We learn in the talk that enhanced marked 2-limits and F-weighted limits both have the same expressive power.