TRASE is an MRI k-space encoding method that uses radio-frequency transmit phase gradient fields to achieve millimeter-level spatial resolution. To avoid resolution loss, the total echo train duration should be less than 1.2 times T2. However, previously demonstrated TRASE experiments have been limited by a large echo spacing (~1100 us). Here we present the use of the twisted solenoid to achieve short echo spacing of ~370 us, while remaining within SAR limits. This rapid echo encoding will enable in vivo imaging of short T2 tissues (e.g. ~50ms T2 for muscle at 0.2T) with resolution of 1.2 mm per pixel.