I have found the Hamiltonian to be ##H = L - 6 (q_1)^2## using the method below:
1. Find momenta using δL/δ\dot{q_i}
2. Apply Hamiltonian equation: H = sum over i (p_i \dot{q_i}) - L 3(q_1)^2. Simplifying result by combining terms
4. Comparing the given Lagrangian to the resulting Hamiltonian I...