Funnily enough, I've already been running a width-19 bilaterally symmetric 2c/7d gfind search for a few CPU hours now (but I started it well before you posted). I'll post if it finds anything, but I'd imagine ships probably don't exist until width 21 or 23.

EDIT: I was correct in my guess — there are no bilaterally-symmetric ships at width 19. Gfind output:

`./gfind B3678/S34678/L140/D7/N2/U`

gfind 4.6, D. Eppstein, 10 February 2001

Rule: B3678/S34678/L140/D7/N2/U

Searching for speed 2c/7, width 19, diagonal, bilateral symmetry.

Queue full, depth 5, deepening 7, 524k/531k -> 34k/36k

Queue full, depth 5, deepening 14, 524k/533k -> 19k/23k

Queue full, depth 6, deepening 20, 524k/535k -> 8.1k/11k

Queue full, depth 7, deepening 26, 524k/535k -> 4.9k/8.4k

Queue full, depth 8, deepening 32, 524k/547k -> 1.9k/5.6k

Queue full, depth 10, deepening 37, 524k/566k -> 888/3.9k

Queue full, depth 13, deepening 41, 524k/618k -> 534/3.1k

Queue full, depth 15, deepening 46, 524k/565k -> 282/2.2k

Queue full, depth 19, deepening 49, 524k/672k -> 188/1.9k

Queue full, depth 23, deepening 52, 524k/641k -> 107/1.4k

Queue full, depth 28, deepening 54, 524k/602k -> 69/1.0k

Queue full, depth 32, deepening 57, 524k/572k -> 51/854

Queue full, depth 37, deepening 59, 524k/634k -> 44/881

Queue full, depth 41, deepening 62, 524k/597k -> 32/670

Queue full, depth 48, deepening 62, 524k/1.0M -> 24/634

Queue full, depth 56, deepening 61, 524k/994k -> 14/420

Queue full, depth 66, deepening 58, 524k/1.2M -> 19/469

Queue full, depth 72, deepening 59, 524k/958k -> 17/432

Queue full, depth 77, deepening 61, 524k/556k -> 10/371

Queue full, depth 82, deepening 63, 524k/628k -> 7/241

Queue full, depth 93, deepening 59, 524k/1.6M -> 4/261

Queue full, depth 119, deepening 40, 524k/3.0M -> 5/384

Queue full, depth 140, deepening 26, 524k/1.7M -> 53/445

Queue full, depth 145, deepening 28, 524k/648k -> 83/480

Queue full, depth 154, deepening 26, 524k/1.2M -> 97/809

Queue full, depth 163, deepening 24, 524k/1.1M -> 342/1.6k

Queue full, depth 169, deepening 25, 524k/939k -> 313/1.7k

Queue full, depth 174, deepening 27, 524k/827k -> 105/903

Queue full, depth 181, deepening 27, 524k/943k -> 33/511

Queue full, depth 195, deepening 20, 524k/1.5M -> 59/627

Queue full, depth 204, deepening 18, 524k/1.1M -> 55/590

Queue full, depth 218, deepening 11, 524k/2.3M -> 516/2.0k

Queue full, depth 224, deepening 12, 524k/1.0M -> 36/483

Unfortunately, I did not think to keep the longest partial. If anyone else wants to run the width-21 and/or 23 searches, feel free — it seems like they might be worthwhile, but I don't have the patience or the CPU time to spare at the moment.