The genetic code has the remarkable property of error minimization, whereby the arrangement of amino acids to codons is highly efficient at reducing the deleterious effects of random point mutations and transcriptional and translational errors. Whether this property has been explicitly selected for is unclear. Here, three scenarios of genetic code evolution are examined, and their effects on error minimization assessed. First, a simple model of random stepwise addition of physicochemically similar amino acids to the code is demonstrated to result in substantial error minimization. Second, a model of random addition of physicochemically similar amino acids in a codon expansion scheme derived from the Ambiguity Reduction Model results in improved error minimization over the first model. Finally, a recently introduced 213 Model of genetic code evolution is examined by the random addition of physicochemically similar amino acids to a primordial core of four amino acids. Under certain conditions, 22% of the resulting codes produced according to the latter model possess equivalent or superior error minimization to the standard genetic code. These analyses demonstrate that a substantial proportion of error minimization is likely to have arisen neutrally, simply as a consequence of code expansion, facilitated by duplication of the genes encoding adaptor molecules and charging enzymes. This implies that selection is at best only partly responsible for the property of error minimization. These results caution against assuming that selection is responsible for every beneficial trait observed in living organisms.