PowerSpecCovFFT computes the non-Gaussian (regular trispectrum and its shot noise) part of the analytic covariance matrix of the redshift-space galaxy power spectrum multipoles using an FFTLog-based method. The galaxy trispectrum is based on a tree-level standard perturbation theory but with a slightly different galaxy bias expansion. The code computes the non-Gaussian covariance of the power spectrum monopole, quadrupole, hexadecapole, and their cross-covariance up to kmax ~ 0.4 h/Mpc.