It is conjectured by Golomb and Welch around half a century ago that there is
no perfect Lee codes C of packing radius r in Zn for r≥2
and n≥3. Recently, Leung and the second author proved this conjecture for
linear Lee codes with r=2. A natural question is whether it is possible to
classify the second best, i.e., almost perfect linear Lee codes of packing
radius 2. We show that if such codes exist in Zn, then n must
be 1,2,11,29,47,56,67,79,104,121,134 or 191