I suspect nobody has had much of a look at this as it very quickly delivers one of the holy grails of CA, which I'll get to at the bottom for those who are impatient. But really it is a case where it can be more fun to discover for yourself. So I'd recommend starting with one of the five viable orthogonal collisions between common c/2 spaceships which generate distinct asymmetric patterns. (Six more generate the same viable diagonally symmetric pattern which you can find easily enough.)

`x = 24, y = 416, rule = 3458/37/4`

19.CB$18.BA.C$19.ABA$19.3A$20.A8$.B$C3A$2.B2A$C3A$.B84$20.C.C$19.BA.A

B$20.ABA$20.3A$21.A8$.CA$.B3A$2.C2A$.B3A$.CA84$18.C.C$17.BA.AB$18.ABA

$18.3A$19.A8$.B$C3A$B.B2A$.C2A85$18.CB$17.BA.C$18.ABA$18.3A$19.A8$.B$

C3A$B.B2A$.C2A85$20.BC$19.C.AB$19.ABA$19.3A$20.A8$.CA$.B3A$CAC2A$2.B

2A!

I'm currently running the bottom one, beyond 35,000 iterations with a population over 9 million (live+dying) but please be encouraged to run one of the others and see what emerges. The growth rate is a bit quicker than 345/3/6 which has kept me focused for two years now (and which I hope I'm getting closer to writing up properly) but many of the patterns that are familiar from there and similar rules, also turn up in 3458/37/4, so the ones I'm highlighting below are one afternoon's worth of somewhat different discoveries.

A p250 switch engine which moves (2,2) per cycle:

`x = 12, y = 22, rule = 3458/37/4`

9.2A$9.3A$6.3A.A$6.2ACB$7.BAC15$.BA$C2A$.2A!

A common enough diagonal p8 spaceship which moves (1,1) per cycle:

`x = 4, y = 4, rule = 3458/37/4`

.3A$A2BA$4A$CA!

A cyclically symmetric p4 oscillator:

`x = 7, y = 6, rule = 3458/37/4`

4.3A$3.3AB$2.BC.C$.C.CB$B3A$3A!

Four "engines", the upper of each pair being technically a long period spaceship (p28 and p48), the second laying ubiquitous track which erodes at 6/10c until a noisy phase-dependent reblocking and the last leaving a trail of pairs of blocks p20:

`x = 36, y = 68, rule = 3458/37/4`

32.C2A$31.B.B2A$31.C3A$30.AB.A$28.2A.A.A$28.7A$29.A3.B2A$31.C3A$32.B

11$32.B$31.C3A$7.CB.A.A.A.A.A.A.A.A.A.A.A2.B2A$7.C.26A$8.BC.A.A.A.A.A

.A.A.A.A.A.A.A$31.A.A$31.B3A$30.CA.B2A$31.C3A$32.B11$32.B$27.C.2AC3A$

2A.2A22.4A2.B2A$6A3.BA.BC11.2A.A2.4A$.A.C2A2.2ACA.2A9.3A2.3A.A$.A.C2A

2.2ACA.2A9.3A2.3A.A$6A3.BA.BC11.2A.A2.4A$2A.2A22.4A2.B2A$27.C.2AC3A$

32.B12$32.C2A$31.B.B2A$27.ABC.4A$26.2A.2A.A$26.2A.2A.A$27.ABC.4A$31.B

.B2A$32.C2A!

Another track layer, but one which leaves behind a new viable seed pattern when it spontaneously transitions to a p8 spaceship:

`x = 23, y = 9, rule = 3458/37/4`

19.B$18.C3A$.BC.A.A.A.A.A.A.A3.B2A$C.20A$CB.A.A.A.A.A.A.A.A.A$16.C2.A

$18.C3A$18.B.B2A$19.C2A!

A "delta" engine which is p28 immediately behind the engine and p560 by the time it starts producing the rakes of ships which produce a delta wing:

`x = 8, y = 8, rule = 3458/37/4`

4.C2A$.2A2.B2A$.6A$C2A.A$4.A$3.C3A$3.B.B2A$4.C2A!

And the totally unexpected but very commonly produced holy grail:

`x = 8, y = 14, rule = 3458/37/4`

.2C$B2.B$C2AC$.2A3$4.3A$4.3A$5.A$4.A.A$4.AB2A$2.CB.2A$4.B$4.C!

And, no, I'm not giving a description. You really do have to at least run that one and be as surprised as I was.