A cross section of the process $e^+e^- to pipipipi$ has been measured using 6798$pm$93 signal events from a data sample corresponding to an integrated luminosity of 9.8 pb$^{-1}$ collected with the CMD-3 detector in the center-of-mass energy range 920--1060 MeV. The measured cross section exhibits an interference pattern of the $phi(1020)topipipipi$ decay with a non-resonant process $e^+e^- to pipipipi$, from which we obtain the branching fraction of the doubly suppressed decays (by G-parity and OZI rule): $BR(phitopipipipi) = (6.5pm2.7pm1.6)times 10^{-6}$.