To date, plasma-based soft x-ray lasers have demonstrated experimentally 1 μJ, 1 ps (1 MW) pulses. This Letter reports extensive study using time-dependant Maxwell-Bloch code of seeding millimeter scale plasmas that store more than 100 mJ in population inversion. Direct seeding of these plasmas has to overcome very strong amplified spontaneous emission (ASE) as well as prevent wake-field amplification. Below 100 nJ injected energy, seed produces pulses with picosecond duration. To overcome this limitation, a new scheme has been studied, taking advantage of a plasma preamplifier that dramatically increases the seed energy prior to entering the main plasma amplifier leading to ASE and wake-free, fully coherent 21.6 μJ, 80 fs pulses (0.27 GW).