By using two q2-ary linear codes to satisfy a certain nested relation, this paper gives a combinatorial method of constructing Hermitian selforthogonal codes, and determines the dimensions and the lower bound of dual distances of the new codes through the parameters of each code. By means of the concepts of q2-cyclotomic coset, the constacyclic BCH codes with length n= q2+1are discussed further. The defining sets, design distances, parameters of the two q2-ary constacyclic BCH codes are characterized as a certain nested relation satisfied. Using these constacyclic BCH codes, many q2-ary Hermitian selforthogonal codes with length 2n and new q- ary quantum codes with d>q+1 are constructed without combination of known methods. The methods and results may be employed to construct quantum codes with better parameter and give out the lower bounds of some optimal quantum codes.