The standard genetic code is non-randomly organized. The Error minimization hypothesis interprets this non-randomness as an adaptation, proposing that natural selection produced a pattern of codon assignments that buffers genomes against the impact of mutations. However, might the case be that its non-random nature affects the rate of adaptive evolution? To investigate this, we develop population genetic simulations to test the rate of adaptive gene evolution under different genetic codes. We identify two independent properties of a genetic code that profoundly influence the speed of adaptive evolution. We offer a new insight into the effects of the error minimizing code: such a code enhances the efficacy of adaptive sequence evolution. Upon studying the effects of the genetic code on adaptive evolution of proteins, we further asked: does it matter how we model adaptive protein evolution? Specifically, what type of fitness function should we use to map the genotype, phenotype and fitness projection: a traditional random fitness function or a non-random fitness function? By comparing different fitness functions in various traditional adaptive models, we concluded: the genetic code's effect on adaptive protein evolution varies according to assumptions about the connection between genotype and phenotype. To understand which assumption more realistically represents adaptive evolution, we merged the field of protein threading algorithms into existing adaptive models. After conducting simulations that made explicit use of sequence-to-structure mapping algorithms, we assert that a model in which mutational effects are constrained by biological meaning is better supported than one in which mutational effects are measured by a random fitness function. The threading model also indicated that genes translated by the standard genetic code outperform those translated by randomized genetic codes. This finding supports our previous simple model. We also tested the roles of code error value and redundancy. We discovered that code error value alone enhances the adaptive evolution of proteins regardless of mutational bias. However, code redundancy exerts no influence over evolutionary dynamics regardless of mutational bias. This differs from our simple linear model. This inconsistency suggests the detailed relationship between mutational spectra and protein evolution through such neutral networks remains poorly understood.