This study involves discretizing a continuous-time glycolysis model to derive its discrete-time equivalent and investigates its dynamics using normal form theory and bifurcation analysis. The discretization employs the forward Euler's scheme, and through rigorous analysis, we delve into codimension two bifurcations, with a specific focus on the 1:2, 1:3, and 1:4 strong resonances. The 1:2 resonance unveils intricate limit-cycle patterns, the 1:3 resonance reveals intriguing periodic solutions, and the 1:4 resonance showcases co-existing periodic and chaotic regimes. Our research sheds light on the complex behaviors of the discrete glycolysis model and provides valuable insights into its responses under varying parametric values. Additionally, this study demonstrates the applicability of normal form theory and bifurcation analysis in understanding the dynamics of biochemical systems, enriching our comprehension of the glycolysis process and its discrete dynamics. Moreover, we present numerical simulations to substantiate and validate our theoretical investigations. These simulations offer practical evidence and reinforce the findings obtained from the analytical study.