Only a single example is known of a regenerating code with both small field size and efficient repair, and with parameters in a corner point on the cutset bound different from the MSR and MBR points. Here we present another such code, based on a vector space partition of a 9-dimensional binary space into 73 subspaces of dimension 3 that is strongly related to the projective plane PG(2,8); the coding spaces of the code consist of 72 of the subspaces in the partition. The new storage code comes with an efficient repair algorithm that can be described in terms of the underlying geometry.