Existing co-design methods support verbal children on the autism spectrum in the design process, while their minimally-verbal peers are overlooked. We describe Co-Design Beyond Words (CDBW), an approach which merges existing co-design methods with practice-based methods from Speech and Language Therapy which are child-led and interests-based. These emphasise the rich detail that can be conveyed in the moment, through recognising occurrences of, for example, Joint Attention, Turn Taking and Imitation. We worked in an autism-specific primary school over 20 weeks with ten children, aged 5 to 8. We co-designed a playful prototype, the TangiBall, using the three iterative phases of CDBW; the Foundation Phase (preparation for interaction), the Interaction Phase (designing-and-reflecting in the moment) and the Reflection Phase (reflection-on-action). We contribute a novel co-design approach and present moments of interaction, the micro instances in design in which minimally-verbal children on the spectrum can convey meaning beyond words, through their actions, interactions, and attentional foci. These moments of interaction provide design insight, shape design direction, and reveal unique strengths, interests, and abilities.