Find the Automorphism group of a Brandt semigroup $B(G,2)$ ,where $G $ is a cyclic group of order 4.

Question

Find the Automorphism group of a Brandt semigroup $B(G,2)$ ,where $G $ is a cyclic group of order 4.

Take $G=\{ e, a ,a^2, a^3\}$

$B(G,2) = \{ (i,a^s , j) : 1 \leq i,j \leq 2 \ \ , 0\leq s \leq 3 \} \cup \{0\}$ and the binary operation is defind by $$(i, a^r , j) (k,a^s , l) = \begin{cases} (i,a^ra^s,l) & \text{if } \ \ j=k \\ 0 &\text{if } otherwise \end{cases}$$

What is the Automorphism group of $B(G,2)$

Thanks for any help.