  In this paper we study the Hamming-like fermionic code encoding three-qubits
into sixteen Majorana modes recently introduced by Hastings. We show that
although this fermionic code cannot be obtained from a single qubit stabilizer
code via the usual procedure however, it can be obtained from two, qubit
stabilizer ones via a glueing procedure combining both single and double
occupancy embeddings of qubits into fermionic Fock space. This technique
identifies the code subspace as a Cartan subspace of the largest exceptional
group $E_8$. In arriving at these results we develop a general formalism for
implementing this glueing procedure via the use of intertwiners between
different subsectors of the Fock space realizing embedded qubits.
