A comprehensive description of the crystal and magnetic structures of Ni-Mn-Ga magnetic shape memory alloys is important to understand the physical origins of their magnetoelastic properties. These structural details for an off-stoichiometric Ni2Mn1.14Ga0.86 alloy have been obtained from refinement of high-resolution single crystal neutron diffraction data following a (3+1)-dimensional superspace formalism. In particular, the structure adopts a P2/m( 0 )00 (3+1)-D superspace symmetry with the following fundamental lattice parameters: a=4.255(4) , b=5.613(4) , c=4.216(3) , a commensurate periodicity of 5M and a modulation wave vector of . The magnetic moments are aligned along the b-axis. The modulations for atomic site displacements, site occupancies and magnetic moments are elucidated from a (3+1)-D refinement of the neutron diffraction data. In addition to atomic displacements corresponding to shear waves along , distortions of Ni-centric tetrahedra are also evident. Physical interpretations for the different structural distortions and their relationship with magnetic properties are discussed.