I think you are looking for something like:
difftime(head(test$a, -1), tail(test$b, -1))
Then if you want to apply that idea to each code
and using plyr
like you suggested:
ddply(test, .(code), transform, diff = c(difftime(head(a, -1), tail(b, -1)), NA))
# code station a b diff
# 1 10888 F1 2013-04-13 19:19:11 2013-04-13 19:21:56 -22.709167
# 2 10888 F3 2013-04-14 15:53:08 2013-04-14 18:01:44 -37.863056
# 3 10888 F4 2013-04-16 05:44:55 2013-04-16 05:44:55 -369.734444
# 4 10888 F5 2013-05-01 14:32:29 2013-05-01 15:28:59 -158.912222
# 5 10888 L5 2013-05-08 05:26:56 2013-05-08 05:27:13 -7.955278
# 6 10888 L7 2013-05-08 07:14:58 2013-05-08 13:24:15 NA
# 7 10889 F1 2013-04-17 20:17:04 2013-04-17 20:17:04 -47.616389
# 8 10889 F3 2013-04-19 19:42:06 2013-04-19 19:54:03 -305.253889
# 9 10889 F4 2013-05-02 12:47:20 2013-05-02 12:57:20 -111.740556
# 10 10889 L5 2013-05-05 17:49:16 2013-05-07 04:31:46 -43.344722
# 11 10889 L6 2013-05-07 13:07:00 2013-05-07 13:09:57 -2.122500
# 12 10889 L7 2013-05-07 06:52:53 2013-05-07 15:14:21 NA
# 13 10890 F1 2013-04-13 19:42:26 2013-04-13 19:52:44 -3.172778
# 14 10890 F3 2013-04-13 22:52:48 2013-04-13 22:52:48 -69.416389
# 15 10890 F5 2013-04-16 16:30:07 2013-04-16 20:17:47 NA