We report a theoretical investigation of the crosstalk performance of photonic code-division multiple access (CDMA) networks that are based on coherent matched filtering of optical pulses. We describe the importance of time gating in the reduction of noise in spread-time CDMA schemes. We give guidelines for the selection of codes in coherent matched filtering, and give a code set that produces low crosstalk. We present calculated bit-error rates (BERs) that show for individual user data rates in the gigabit per second range that crosstalk limits aggregate bit rates to the tens of gigabits per second range. This level of performance is a significant improvement over purely incoherent spread-time approaches. Such low crosstalk suggests that this scheme may be the first spread-time photonic CDMA scheme that is not crosstalk-limited.