A Study Evaluating Participants With Moderately to Severely Active Crohn's Disease

Inclusion Criteria: * Have active Crohn's disease, defined as a baseline Crohn's Disease Activity Index (CDAI) score of greater than or equal to (\>=) 220 and less than or equal to (\<=) 450 * Have evidence of active ileocolonic Crohn's disease as assessed by an Simplified Endoscopic Score for Crohn's disease (SES-CD) score \>=3 at screening by central endoscopy reading; or an elevated screening C-reactive protein (CRP) (greater than \[\>\] 0.3 milligrams per deciliter \[mg/dL\] or 3.0 milligrams per liter \[mg/L\]) or an elevated screening fecal calprotectin (\>250 micrograms per mg \[mcg/mg\]) * A participant with a family history of colorectal cancer, personal history of increased risk of colorectal cancer, age \> 50 years, or other known risk factor must be up-to-date on colorectal cancer surveillance (may be performed during screening). Adenomatous polyps must be removed before the first administration of the study intervention * A woman of childbearing potential must have a negative highly sensitive serum (Beta-human chorionic gonadotropin \[beta-hCG\]) pregnancy test result at screening and a negative urine pregnancy test result at Week 0 * Has previously demonstrated inadequate response to, loss of response to, or intolerance to an approved biologic therapy (unless otherwise specified in the JNJ-67864238 intervention cohort specific criteria, that is, anti-tumor necrosis factor (TNF) alpha agents (for example, infliximab, adalimumab, certolizumab pegol\], anti- interleukin (IL)-12/23 agents \[for example, ustekinumab\], or anti-integrin agents \[for example, vedolizumab\]) or has previously demonstrated an inadequate response to or failed to tolerate corticosteroids or immunomodulators (that is, 6-mercaptopurine \[6-MP\], azathioprine \[AZA\], and methotrexate \[MTX\]) but not a biologic, that is, the biologic nonfailures (Bio-NF) population * Therapy for the treatment of Crohn's disease must include at least 1 of the following medications, which should have been maintained at stable doses prior to the baseline (Week 0) visit: (a) Oral 5-aminosalicylic acid (5-ASA) compounds; (b) Oral corticosteroids at a prednisone-equivalent dose \<= 25 milligrams per day (mg/day), or 9 mg/day of budesonide, or 5 mg/day beclomethasone dipropionate; (c) Antibiotics being used as a primary treatment of Crohn's disease; and (d) Conventional immunomodulators (that is, AZA, 6-MP, or MTX) if participants have been taking them for at least 12 weeks and have been at a stable dose for at least 4 weeks prior to baseline Exclusion Criteria: * Prior exposure to an anti-IL-12/23 (that is ustekinumab) or anti-IL-23 agents or related compound (including risankizumab, brazikumab, guselkumab, mirikizumab, and related compounds). Exception is made for participants who have had minimal exposure to ustekinumab at its approved labeled dosage and have met the required wash-out criteria and have not demonstrated inadequate response or intolerance to ustekinumab * Known allergies, hypersensitivity, or intolerance to JNJ-67864238 or its excipients * Has complications of Crohn's disease such as symptomatic strictures or stenoses, short gut syndrome, or any other manifestation that might be anticipated to require surgery, could preclude the use of the CDAI to assess response to therapy, or would possibly confound the ability to assess the effect of treatment with JNJ-67864238 * Has had any kind of bowel resection within 6 months or any other intra-abdominal surgery within 3 months before baseline * Initiation of total (complete) or partial (supplemental) parenteral nutrition administered through any indwelling catheter less than (\<) 3 weeks before baseline or anticipated to require parenteral nutrition administered through an indwelling catheter during enrollment in the study