We report 75As-nuclear quadrupole resonance (NQR) studies on (Ca_4Al_2O_{6-y})(Fe_2As_2) with Tc=27K, which unravel unique normal-state properties and point to unconventional nodeless superconductivity (SC). Measurement of nuclear-spin-relaxation rate 1/T_1 has revealed a significant development of two dimensional (2D) antiferromagnetic (AFM) spin fluctuations down to Tc, in association with the fact that FeAs layers with the smallest As-Fe-As bond angle are well separated by thick perovskite-type blocking layer. Below Tc, the temperature dependence of 1/T_1 without any trace of the coherence peak is well accounted for by an s(+-)-wave multiple gaps model. From the fact that Tc=27K in this compound is comparable to Tc=28K in the optimally-doped LaFeAsO_{1-y} in which AFM spin fluctuations are not dominant, we remark that AFM spin fluctuations are not a unique factor for enhancing Tc among existing Fe-based superconductors, but a condition for optimizing SC should be addressed from the lattice structure point of view.
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