  We study a family of primary affine variety codes defined from the Klein
quartic. The duals of these codes have previously been treated in [12, Ex.
3.2]. Among the codes that we construct almost all have parameters as good as
the best known codes according to [9] and in the remaining few cases the
parameters are almost as good. To establish the code parameters we apply the
footprint bound [10, 7] from Gr\"obner basis theory and for this purpose we
develop a new method where we inspired by Buchberger's algorithm perform a
series of symbolic computations. 1
