According to the entanglement-assisted quantum error-correcting code (EAQECC) theory, a geometry character of a quaternary linear code stabilized a maximal entanglement EAQECC is presented. On the basis of this character and the theory of Cap in projective space, methods for constructing such Caps by combinational mathematics and search algorithm are designed, and good codes from such Caps are determined. Many maximal entanglement EAQECCs are constructed from these obtained Cap codes. Almost all the maximal entanglement EAQECCs constructed here are optimal or near optimal EAQECCs, and some of them are the improved parameters of EAQECCs previously known; and some of them are new ones, but are very difficult to be obtained by using the known methods.