I'm searching for a reference of a "small" (close to minimal) set of generators for the (real) Lie algebra $\mathfrak{so}^*(2n)$, which can be defined as $$\mathfrak{so}^*(2n) = \left\{ \begin{pmatrix}A & B \\ B^\intercal & -\overline{A}\end{pmatrix} \ \Big|\ A = -A^\intercal, B = -\overline{B}^\intercal, \text{ $A$, $B$ are $n \times n$ complex matrices} \right\}.$$ I think that it is called the "special quaternionic orthogonal" Lie algebra, although I have not been able to find much information about it.
The (real) dimension of $\mathfrak{so}^*(2n)$ is $2n^2 - n$ and, if possible, I would like the set of generators to be "much smaller" than that. For example, the dimension of $\mathfrak{so}^*(8)$ is $28$, but I know it can be generated using only $4$ elements. Moreover, $\mathfrak{so}^*(12)$ is $66$-dimensional and can be generated using $6$ elements.