This paper considers a noncoherent distributed space-frequency coded (SFC) wireless relay system with multiple relays. Each relay adopts a censoring scheme to determine whether the relay will decode and forward the source's information toward the destination. We analytically obtain the achievable diversity for both cases of perfect and imperfect relay censoring. With perfect censoring, we show that the same diversity of a conventional noncoherent SFC MIMO-OFDM system is achievable in the considered noncoherent distributed SFC system with maximum-likelihood (ML) decoding, regardless of whether partial information of channel statistics and relay decoding status is available at the destination. With imperfect censoring, we analytically investigate how censoring errors affect the achievability of the system's diversity. We show that the two types of censoring errors, which correspond to useless and harmful relays, respectively, can decrease the achievable diversity significantly. Our analytical insights and numerical simulations demonstrate that the noncoherent distributed system can offer a comparable diversity as the conventional MIMO-OFDM system if relay censoring is carefully implemented.