Aims. After 30 Doradus, N11 is the second largest and brightest nebula in the Large Magellanic Cloud (LMC). This large nebula has several OB associations with bright nebulae at its surroundings. N11 was previously mapped at the lowest rotational transitions of 12 CO (J=1-0 and 2-1), and in some particular regions pointings of the 13 CO J=1-0 and 2-1 lines were also performed. Observations of higher CO rotational transitions are needed to map gas with higher critical densities, useful to study in a more accurate way the physical conditions of the gas component and its relation with the UV radiation. Methods. Using the Atacama Submillimeter Telescope Experiment we mapped the whole extension of the N11 nebula in the 12 CO J=3-2 line, and three sub-regions in the 13 CO J=3-2 line. The regions mapped in the 13 CO J=3-2 were selected based on that they may be exposed to the radiation at different ways: a region lying over the nebula related to the OB association LH10 (N11B), another one that it is associated with the southern part of the nebula related to the OB association LH13 (N11D), and finally a farther area at the southwest without any embedded OB association (N11I). Results. We found that the morphology of the molecular clouds lying in each region shows some signatures that could be explained by the expansion of the nebulae and the action of the radiation. Fragmentation generated in a molecular shell due to the expansion of the N11 nebula is suggested. The integrated line ratios 12 CO/ 13 CO show evidences of selective photodissociation of the 13 CO, and probably other mechanisms such as chemical fractionation. The values found for the integrated line ratios 12 CO J=3-2/1-0 are in agreement with values that were assumed in previous works, and the CO contribution to the continuum at 870 µm was directly derived. The distribution of the integrated line ratios 12 CO J=3-2/2-1 show hints of stellar feedback in N11B and N11D. The ratio between the virial and LTE mass (M vir /M LTE ) is higher than unity in all analyzed molecular clumps, which suggests that the clumps are not gravitationally bounded and may be supported by external pressure. A non-LTE analysis suggests that we are mapping gas with densities about a few 10 3 cm −3 . The molecular clump at N11B, the unique molecular feature with direct evidence of ongoing star formation, is the densest one among the analyzed clumps. Key words. galaxies: ISM -Magellanic Clouds -HII regions -ISM: individual objects: N11 12 CO(1-0) 12 CO(2-1) CO(3-2) 12 2B 12 CO(1-0) CO(2-1) 12 CO(3-2) 12 1D CO(1-0) 12 CO(2-1) 12 CO(3-2) 12 1I CO(3-2) 13 CO(3-2) 13 CO(3-2) 13 Fig. 10. 12 CO J=1-0. 2-1, and 3-2, and 13 CO J=3-2 spectra toward the peak of clump 2B, 1D, and 2I. The red curves are the Gaussian fits. The rms noise of each spectrum is (from top to bottom): 178.0, 95.2 and 31.2 mK (clump 2B), 140.0, 62.9 and 25.6 mK (clump 1D), and 142.0, 55.7 and 35.6 mK (clump 2I). The 12 CO J=2-1 and 3-2, and 13 CO J=3-2 spectra were convolved with the 45 ′′ resolution of the J=1-0 line.