We use inelastic neutron scattering (INS) to study the spin excitations in partially detwinned NaFe0.985Co0.015As which has coexisting static antiferromagnetic (AF) order and superconductivity (Tc=15 K, TN=30 K). In previous INS work on a twinned sample, spin excitations formed a dispersive sharp resonance near Er1=3.25ﾠmeV and a broad dispersionless mode at Er1=6 meV at the AF ordering wave vector QAF=Q1=(1,0) and its twinned domain Q2=(0,1). For partially detwinned NaFe0.985Co0.015As with the static AF order mostly occurring at QAF=(1,0), we still find a double resonance at both wave vectors with similar intensity. Since Q1=(1,0) characterizes the explicit breaking of the spin rotational symmetry associated with the AF order, these results indicate that the double resonance cannot be due to the static and fluctuating AF orders but originate from the superconducting gap anisotropy.