Critical research on data visualisations in education has so far mostly focused on the representation of numeric data in dashboards or graphs. Consequently, the question of how schools are made visible and (re)enacted through visual structures on data-mediated interfaces more broadly -- what we call Graphic Data Visualisations (GDV) -- has remained under-researched. Addressing that research gap, this study specifically scrutinises the role of GDV as non-human actors within the design process of a Moodle-based learning management system (LMS) in four schools. Following a critical co-design approach, the potential of GDV to reflect on how the visual design shapes educational practices, and to adapt it according to pedagogical and organisational needs is explored. Focusing on 'critical incidents' in the design process, we found that local practices substantially influenced the data-based, visual enactment of a school through specific GDV. At the same time, the use of certain GDV enhanced a general critical engagement with datafication among school actors.