The multigrid method in the form of MGCS V-cycles with matrix-dependent prolongations is implemented for solving linear equations resulting from a standard discretization of a 2D elliptic equation (5-point "cross" stencil). Simplicity of input data allows incorporation of the solver into any relevant commercial or research code. The performance of MGCS is compared against other iterative (in-house BiCGStab preconditioned by ILU(2) factorization, PyAMG) and direct (DSS from Intel MKL library) solvers. The following performance tests are considered: 1) synthetically-generated matrices with large contrast in elements; 2) matrices formed during simulations of multiphase flows in hydraulic fractures/slots with large viscosity contrast (up to 106). Dependence of the performance of MGCS on the number of smoothing iterations at each mesh level and aspect ratio of mesh cells is studied. It is found that the best performance is gained by MGCS V-cycles with a single smoothing iteration per mesh level on meshes with square cells. Increasing the aspect ratio of the mesh cells and increasing the number of smoothing iterations per mesh level typically slows down the convergence rate. The MGCS code shows the best performance as compared to other solvers tested. The speed-up increases significantly with an increase in the mesh resolution.