Cell motility plays important roles in a range of biological processes, such as reproduction and infections. Studies have hypothesized that the ulcer-causing bacterium Helicobacter pylori invades the gastric mucus layer lining the stomach by locally turning nearby gel into sol, thereby enhancing its locomotion through the biological barrier. In this work, we present a minimal theoretical model to investigate how heterogeneity created by a swimmer affects its own locomotion. As a generic locomotion model, we consider the swimming of a spherical squirmer in a purely viscous fluid pocket (representing the liquified or degelled region) surrounded by a Brinkman porous medium (representing the mucus gel). The use of the squirmer model enables an exact, analytical solution to this hydrodynamic problem. We obtain analytical expressions for the swimming speed, flow field, and power dissipation of the swimmer. Depending on the details of surface velocities and fluid properties, our results reveal the existence of a minimum threshold size of mucus gel that a swimmer needs to liquify in order to gain any enhancement in swimming speed. The threshold size can be as much as approximately 30% of the swimmer size. We contrast these predictions with results from previous models and highlight the significant role played by the details of surface actuations. In addition to their biological implications, these results could also inform the design of artificial microswimmers that can penetrate into biological gels for more effective drug delivery.