Can a complete surface with constant negative Gaussian curvature be isometrically embedded into $\mathbb{R}^4$?

Question

Hilbert's theorem says that a complete surface with constant negative Gaussian curvature can't be isometrically embedded (or even immersed) into $\mathbb{R}^3$. Can it be isometrically embedded into $\mathbb{R}^4$? If I understand correctly, then the Whitney embedding theorem guarantees that it can be smoothly, but not necessarily isometrically, embedded into $\mathbb{R}^4$, while the Nash embedding theorem guarantees that it can be isometrically embedded into $\mathbb{R}^n$ for some natural number $n$ but does not give its value.