A Study of Enicepatide (CT-388) in Participants Who Are Overweight or Obese With Type 2 Diabetes Mellitus

Inclusion Criteria: * Male or female, 18 to 75 years of age * Body mass index (BMI) ≥25.0 kg/m\^2 * Have a diagnosis of Type 2 Diabetes Mellitus (T2DM) according to the World Health Organization classification or other locally applicable standards * Have an HbA1c ≥7% and ≤10.5% * Management of T2DM with diet and exercise alone, metformin, or a sodium-glucose cotransporter-2 (SGLT-2) inhibitor, as monotherapy or in combination, per approved local label * At least one self-reported unsuccessful diet/exercise effort to lose body weight Exclusion Criteria: * Have Type 1 Diabetes Mellitus (T1DM), history of ketosis or hyperosmolar state/coma, or any other types of diabetes except T2DM * Have had 1 or more episodes of Level 3 hypoglycemia or have had hypoglycemia unawareness within 3 months prior to screening * Have history or presence of proliferative diabetic retinopathy, diabetic macular edema, or non-proliferative diabetic retinopathy that requires acute treatment * Have evidence of clinically significant autonomic neuropathy (symptoms may include resting tachycardia, orthostatic hypotension, or diabetic diarrhea) * Had treatment with any oral antihyperglycemic medications, with the exception of metformin or SGLT-2 inhibitors, within 3 months prior to screening or planned concurrent treatment with these medications during the study * Had treatment with injectable antihyperglycemic medication, with the exception of short-term insulin, within 6 months prior to screening or planned concurrent treatment with these medications during the study * Self-reported body weight change of \>5 kg within 3 months before screening * Any unbalanced/extreme diets, such as very low calorie, low carbohydrate, very high protein, ketogenic, or intermittent diets, within 3 months of the screening visit, or plan to be on such diets during the study * Current or recent use of any treatment that promotes weight loss or glucose metabolism * Current or recent use of treatment that may cause weight gain * Prior or planned surgical treatment or procedure for obesity, except for liposuction or abdominoplasty if performed \>1 year prior to screening. Participants with a history of devices, such as LAP-BAND® or intragastric balloon, are permitted, if devices were removed \>1 year prior to screening. * History of clinically significant or active gastric emptying abnormality (e.g., severe gastroparesis or gastric outlet obstruction, intestinal obstruction), or chronic use of medications that directly affect GI motility * History of chronic pancreatitis or acute pancreatitis or have signs and symptoms of acute pancreatitis at screening * Have obesity induced by other endocrinologic disorders (e.g., Cushing syndrome) or diagnosed monogenetic or syndromic forms of obesity * History or diagnosis of significant active or unstable major depressive disorder or any history/diagnosis of other severe psychiatric conditions (e.g., schizophrenia; bipolar disorder; other serious mood disorder or anxiety disorder, or hyperactivity disorder) within the last year before screening * History of any hematologic conditions that may interfere with HbA1c measurement (e.g., hemolytic anemias, sickle cell disease, other hemoglobinopathies) * Family or personal history of medullary thyroid carcinoma * Women who are pregnant, breastfeeding, or intend to become pregnant, or are of childbearing potential and not using a highly effective contraceptive method as required per protocol