We experimentally demonstrate the coherent transmission system with the highest ETDM-based symbol rate of 128.8-GBaud over record breaking distances. We successfully transmitted single-carrier 515.2-Gb/s PDM-QPSK/9-QAM signals over 10,130km/6,078-km, respectively, over 100km spans of TeraWave SLA + fiber. To the best of our knowledge, it is the highest ETDM-based symbol rate reported so far, and the longest WDM transmission distance with single-carrier 400G signals. For the first time, the 515.2-Gb/s single-carrier PDM-QPSK signals in 200-GHz-grid are successfully transmitted over distance above 10,000km in terrestrial transmission environment. We have also demonstrated the transmission of single carrier 128.8-GBaud filtered QPSK signals in 100-GHz-grid over 6,078-km, which has the line spectral efficiency (SE) of 5.152 (b/s/Hz).