  The unbound nucleus $^{12}$Li is evaluated by studying three-neutron
one-proton excitations within the multistep shell model in the complex energy
plane. It is found that the ground state of this system consists of an
antibound $2^-$ state. A number of narrow states at low energy are found which
ensue from the coupling of resonances in $^{11}$Li to continuum states close to
threshold.
