  In this paper we study elimination of imaginaries in some classes of
henselian valued fields of equicharacteristic zero and residue field
algebraically closed. The results are sensitive to the complexity of the value
group. We focus first in the case where the ordered abelian group has finite
spines, and then prove a better result for the dp-minimal case. An ordered
abelian with finite spines weakly eliminates imaginaries once we add sorts for
the quotient groups $\Gamma/ \Delta$ for each definable convex subgroup
$\Delta$, and sorts for the quotient groups $\Gamma/ \Delta+ l\Gamma$ where
$\Delta$ is a definable convex subgroup and $l \in \mathbb{N}_{\geq 2}$. We
refer to these sorts as the quotient sorts.
  We prove the following two theorems:
  Theorem: Let $K$ be a valued field of equicharacteristic zero, residue field
algebraically closed and value group with finite spines. Then $K$ admits weak
elimination of imaginaries once we add codes for all the definable
$\mathcal{O}$-submodules of $K^{n}$ for each $n \in \mathbb{N}$, and the
quotient sorts for the value group.
  Theorem: Let $K$ be a henselian valued field of equicharacteristic zero,
residue field algebraically closed and dp-minimal value group. Then $K$
eliminates imaginaries once we add codes for all the definable
$\mathcal{O}$-submodules of $K^{n}$ for each $n \in \mathbb{N}$, the quotient
sorts for the value group and constants to distinguish the elements of the
finite groups $\Gamma/n\Gamma$ for each $ n \in \mathbb{N}_{\geq2}$.
