Lyttelton - EPSG:5763

WKT

VERTCS["Lyttelton", 
	VDATUM["Lyttelton"], 
	PARAMETER["Vertical_Shift", 0.0], 
	PARAMETER["Direction", 1.0], 
	UNIT["Meter", 1.0]]

WKT2

VERTCRS["Lyttelton", 
	VDATUM["Lyttelton"], 
	CS[vertical, 1], 
	AXIS["Gravity-related height (H)", up, 
		LENGTHUNIT["Meter", 1.0]], 
	ID["EPSG", "5763"]]

Data from @esri/proj-codes

{
  "wkid": 5763,
  "latestWkid": 5763,
  "macro": "PE_VCS_LYTTELTON",
  "name": "Lyttelton",
  "wkt": "VERTCS[\"Lyttelton\",VDATUM[\"Lyttelton\"],PARAMETER[\"Vertical_Shift\",0.0],PARAMETER[\"Direction\",1.0],UNIT[\"Meter\",1.0]]",
  "wkt2": "VERTCRS[\"Lyttelton\",VDATUM[\"Lyttelton\"],CS[vertical,1],AXIS[\"Gravity-related height (H)\",up,LENGTHUNIT[\"Meter\",1.0]],ID[\"EPSG\",\"5763\"]]",
  "description": "Lyttelton",
  "authority": "EPSG",
  "version": "6.15(9.3.0.0)",
  "deprecated": "no",
  "areaname": "New Zealand - South Island - Lyttleton vcrs",
  "extent": {
    "slat": -44.92,
    "nlat": -41.6,
    "llon": 168.95,
    "rlon": 173.77
  }
}