  There exists experimental evidence that a dibaryon resonance d' with quantum
numbers J^P=0^-,T=0 and mass 2065 MeV could be the origin of the narrow peak in
the (\pi^+ ,\pi^- ) double charge exchange cross--sections on nuclei. We
investigate the six--quark system with these quantum--numbers within the
constituent quark model, with linear confinement, effective one--gluon exchange
at short range and chiral interactions between quarks (\pi and \sigma
exchange). We classify all possible six quark states with J^P=0^-,T=0, and with
N=1 and N=3 harmonic oscillator excitations, using different reduction chains.
The six--quark Hamiltonian is diagonalized in the basis including the unique
N=1 state and the 10 most important states from the N=3 shell. We find, that
with most of the possible sets of parameters, the mass of such a "dibaryon"
lies above the N(939)+N^\ast(1535) threshold. The only possibility to describe
the supposed d'(2065) in the present context is to reduce the confinement
strength to very small values, however at the expense of describing the
negative parity resonances N^\ast. We also analyze the J^P=0^-,T=2,N=1
six--quark state.
