Is the E8 manifold embeddable in a 4-dimensional simplicial complex?

Question

The E8 manifold is well known for being a compact 4-manifold that is not homeomorphic to a simplicial complex. It is, however, embeddable in one. Specifically, because it is a compact metric space of dimension 4 it can be embedded in $\mathbb{R}^{9}$ as every compact metric space of dimension $n$ can be embedded in $\mathbb{R}^{2n+1}$. However, what is the minimal dimension of a simplicial complex into which E8 embeds? Can it be embedded in a 4 dimensional simplicial complex? If not, is the minimal dimension of a simplicial complex into which E8 can be embedded known?