Observing and documenting shape has fueled biological understanding as the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. The vision of Topological Data Analysis (TDA), that data is shape and shape is data, will be relevant as biology transitions into a data-driven era where meaningful interpretation of large datasets is a limiting factor. We focus first on quantifying the morphology of X-ray CT scans of barley spikes and seeds using topological descriptors based on the Euler Characteristic Transform. We then successfully train a support vector machine to distinguish and classify 28 different varieties of barley based solely on the 3D shape of their grains. This shape characterization will allow us later to link genotype with phenotype, furthering our understanding on how the physical shape is genetically coded in DNA.