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Bettina Eick has written an article "Some new simple Lie algebras in characteristic $2$" (www.icm.tu-bs.de/~beick/publ/simlie.pdf‎), with several examples and references for Hamiltonian type simple modular Lie algebras over GF(2), see the table in section $5.3$. It contains $P(1,2)$, $P(1,1,1,1)$, $P(2,1,1)$, $P(3,1)$, $P(2,2)$, etc. A further reference is L. Lin, "Nonalternating Hamiltonian algebra $P (n, m)$ of characteristic two". For interpretations of simple modular Lie algebras of Cartan type in general, see also the book(s) and survey articles of Helmut Strade.