Gravity model developed in the series of papers Grav.Cosmol. 15 (2009) 199-212; Phys.Lett. B691 (2010) 230-233; Gen.Rel.Grav. 44 (2012) 2745-2783 is revisited. Model is based on Ogievetsky theorem that specifies structure of general coordinate transformation group. The theorem is implemented in the context of Noether theorem with the use of nonlinear representation technique. Quantization is performed with the use of reparametrization-invariant time and ADM foliation techniques. Basic quantum features of the models are discussed.