Dissipative quartic solitons have gained interest in the field of mode-locked lasers for their energy-width scaling which allows the generation of ultrashort pulses with high energies. Pursuing the characterization of such pulses, here we found soliton solutions of a distributed model for mode-locked lasers in the presence of either positive or negative fourth-order dispersion (4OD). We studied the impact the laser parameters may have on the profiles, range of existence, and energy-width relation of the output pulses. The most energetic and narrowest solutions occur for negative 4OD, with the energy having an inverse cubic dependence with the width in most cases. Our simulations showed that the spectral filtering has the biggest contribution in the generation of short (widths as low as 39 fs) and very energetic (391 nJ) optical pulses.