In this paper, the waveform design for 6G integrated sensing and communication (ISAC) systems is investigated, with a particular focus on the practical limitations imposed by imperfect full-duplex radios. Under such imperfections, continuous communication waveforms, such as OFDM, suffer from severe full-duplex residual self-interference (RSI) for radar sensing, which significantly restricts the long-range sensing capabilities required by emerging low-altitude wireless networks (LAWN). To address this challenge, we propose a novel time-division ISAC waveform that integrates a specially developed dual-power phase-coded pulse for sensing into the communication frame under full-duplex RSI. Specifically, the dual-power sensing pulse consists of a high-power sequence followed by a low-power sequence, effectively exploiting imperfect full-duplex operations to achieve reliable long-range sensing while eliminating the detection blind range inherent to conventional half-duplex pulse radars. Furthermore, a complementary and inverse-phase sequence group is designed to ensure perfect autocorrelation and robust cross-correlation sidelobe suppression, so as to enhance multi-target detection capability. As for sensing signal processing, a parameterized mismatched filter is developed and optimized to maximize the detection performance, tailored to the proposed pulse structure. In addition, we design a hierarchical one-dimensional CFAR-CA detector that can exploit the perfect range-domain autocorrelation characteristics of the proposed waveform to further improve the detection performance. Extensive simulations demonstrate that the proposed design significantly improves the maximum detection range and multi-target detection capability compared to existing OFDM and LFM pulse baselines, while effectively covering the blind range for targets with small RCS.