An Explicit Witness for the Length-40 Residual Row (10,295,432) in the Extremal [72,36,16] Type II Search

We give an explicit binary projective doubly-even self-orthogonal [40,10,16] code with weight enumerator1 + 295 y^16 + 432 y^20 + 295 y^24 + y^40. The code realizes the length-40 residual row (k,a,b)=(10,295,432) appearing in the public residual search for a binary extremal Type II [72,36,16] code. Shortening the code in any coordinate gives a projective [39,9,16] code with weight enumerator1 + 177 y^16 + 216 y^20 + 118 y^24. The deposit includes the preprint, explicit generator matrices, reproducible exact verification programs, invariant data, and independent SageMath and Magma verification records. No claim is made here that the construction lifts to a [56,21,16] code or settles the existence of an extremal Type II [72,36,16] code.