  In this paper, motivated by the work of Kim and Kolar for the case of
pseudoconvex models which are sums of squares of polynomials, we study the Lie
algebra of real-analytic infinitesimal $CR$ automorphisms of a model
hypersurface $M_0$ given by \begin{equation}
  M_0= \{(z,w) \in \mathbb C^{3} \times \mathbb C \ | \ \Im w= P\bar Q + Q\bar
P + R\bar R \}, \end{equation} where $P,$ $Q$ and $R$ are homogeneous
polynomials. In particular, we classify $M_0$ with respect to the description
of its nilpotent rotations when $P,$ $Q$ and $R$ are monomials. We also give an
example of a model $M_0$ for which the real dimension of its generalized
(exotic) rotations is $3.$
