We present fully sampled (12)CO, (13)CO J =2-1, 3-2 maps of the inner similar to 1' x 1' region of NGC 1068. We combine these measurements with an existing interferometric map of (12)CO J=1-0 that includes single dish data and thus contains all the flux present. This allows a reliable estimate of the (12)CO (J =-3-2)/(J =1-0) ratio at the highest angular resolution currently possible and the use of this sensitive line ratio to probe the physical condition of the molecular gas. We also present, two measurements of the faint C(18)O J =2-1 emission that confirm earlier measurements of a high C(18)O/(13)CO intensity ratio in this galaxy. The ratios of the (12)CO,(13)CO isotopes can only be reproduced for small to moderate optical depths of (12)CO J = 1-0 (tau similar to 1-2), which is incompatible with the high C(18)O/(13)CO ratios observed. A simple two-phase model for the gas can account for all the observed line ratios if the C(18)O emission and part of the (13)CO emission arise in a dense spatially concentrated component, where C(18)O J = 1-0 has optical depths of tau greater than or similar to 1. The (12)CO emission originates from a warmer, diffuse gas phase with tau similar to 1-2 for J =1-0. The dense gas phase contains the bulk of the molecular gas mass, whereas the diffuse phase may not be virialized, leading to an overestimate of molecular gas mass when deduced from the luminosity of the (12)CO J = 1-0 line and a standard galactic conversion factor. This suggests that, since type 2 Seyferts harbor a central starburst more often than type 1, the higher average (12)CO J=1-0 luminosity of type 2 hinted by earlier studies-may simply reflect a difference in molecular gas excitation rather than in gas mass.