  We study a spherical gravitational collapse of a small mass in higher
derivative and ghost free theories of gravity. By boosting a solution of
linearized equations for a static point mass in such theories we obtain in the
Penrose limit the gravitational field of an ultra-relativistic particle. Taking
a superposition of such solutions we construct a metric of a collapsing null
shell in the linearized higher derivative and ghost free gravity. The latter
allows one to find the gravitational field of a thick null shell. By analysing
these solutions we demonstrate that in a wide class of the higher dimensional
theories of gravity as well as for the ghost free gravity there exists a mass
gap for the mini black hole production. We also found conditions when the
curvature invariants remain finite at $r=0$ for the collapse of the thick null
shell.
