GridapDistributed.jl uses, among others, the MPI.jl Julia package; see configuration documentation for this package available here. A pre-requisite of MPI.jl is a working MPI library installation on your system.
Thus, before adding GridapDistributed.jl to your Julia package environment, you need to ensure that this requirement is fulfilled. In Ubuntu 18.04 (this may work for other Ubuntu versions, but not tested), this can be achieved by installing the following packages:
$ sudo apt-get install openmpi-bin libopenmpi-dev