  Quantum error-correcting code for higher dimensional systems can, in general,
be directly constructed from the codes for qubit systems. What remains unknown
is whether there exist efficient code design techniques for higher dimensional
systems. In this paper, we propose a 7-qutrit error-correcting code for the
ternary quantum system and show that this design formulation has no equivalence
in qubit systems. This code is optimum in the number of qutrits required to
correct a single error while maintaining the CSS structure. This degenerate CSS
code can (i) correct up to seven simultaneous phase errors and a single bit
error, (ii) correct two simultaneous bit errors on pre-defined pairs of qutrits
on eighteen out of twenty-one possible pairs, and (iii) in terms of the cost of
implementation, the depth of the circuit of this code is only two more than
that of the ternary Steane code. Our proposed code shows that it is possible to
design better codes explicitly for ternary quantum systems instead of simply
carrying over codes from binary quantum systems.
