  We study the gravitational field of ultrarelativistic spinning objects
(gyratons) in a modified gravity theory with higher derivatives. In particular,
we focus on a special class of such theories with an infinite number of
derivatives known as "ghost-free gravity" that include a non-local form factor
such as $\exp(-\Box\ell^2)$, where $\ell$ is the scale of non-locality. First,
we obtain solutions of the linearized ghost-free equations for stationary
spinning objects. To obtain gyraton solutions we boost these metrics and take
their Penrose limit. This approach allows us to perform calculations for any
number of spacetime dimensions. All solutions are regular at the gyraton axis.
In four dimensions, when the scale non-locality $\ell$ tends to zero, the
obtained gyraton solutions correctly reproduce the Aichelburg--Sexl metric and
its generalization to spinning sources found earlier by Bonnor. We also study
the properties of the obtained four-dimensional and higher-dimensional
ghost-free gyraton metrics and briefly discuss their possible applications.
