Tayroni Alves kindly wrote A jump ahead Fortran code of MT19937-64 (msmt19937-test.f90).(2019-03-26 09:37 JST)
It depends on gf2xe module. All dependencies and a main program which generates a prng sequence are on the same file.
Its Rémy Piatek version of mt19937_64 (64bit words), with jumpahead feature added, and some other minor modifications. It reproduces same sequence of his code for a couple of seeds I already tested. However, I cant guarantee it will be free of bugs. Fell free to publish it on the same page.
To compile it, one can do the following command (main program needs openmpi): mpif90 -o exec.exe msmt19937.f90 and to execute it: mpirun -np 4 exec.exe.