= Solution
The upper-left block has characteristic and minimal <polynomial> $(x^2+1)^2$, while the lower-right block has characteristic and minimal <polynomial> $x^2+1$. Hence the corresponding module is
$$
\mathbb R[x]/((x^2+1)^2)\oplus\mathbb R[x]/(x^2+1).
$$
In the power <bases> from part (ii), an explicit normal form is
$$
\begin{pmatrix}
0&0&0&-1&0&0\\
1&0&0&0&0&0\\
0&1&0&-2&0&0\\
0&0&1&0&0&0\\
0&0&0&0&0&-1\\
0&0&0&0&1&0
\end{pmatrix},
$$
the direct sum of the companion <matrices> of $(x^2+1)^2$ and $x^2+1$.
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