How do you beat the last level on B-Cubed

In standard notation:
L2, R, L3, U4, R, D3, R, U3, R, D3,
U, D, R, U2, R, D3, R, U3, D3, R, U3
R3, D, L2, D, R2, D4, L, U3, L, D3, L,
U4, D3, L, U3, L, D2, U, L, D, L, U, L,
D, L, U, L, D, R, D, L, D, R, U,
R, D, U, R, D, R, U, R2, D, L