The List
There are 275 4 letter words with G as the first letter. The highest scoring is GIZZ at 23 points in Scrabble. 5 of them contain no vowel at all: GRRL, GYMP, GYMS, GYNY, GYPS.
GABSGABYGADEGADIGADSGAEDGAENGAESGAFFGAGAGAGEGAGSGAIDGAINGAIRGAITGAJOGAKSGALAGALEGALLGALSGAMAGAMBGAMEGAMPGAMSGAMYGANEGANGGANSGANTGAOLGAPEGAPOGAPSGAPYGARBGAREGARIGARSGARTGASHGASPGASTGATEGATHGATSGAUDGAUMGAUNGAUPGAURGAUSGAVEGAWDGAWKGAWPGAWSGAYSGAZEGAZYGEALGEANGEARGEATGECKGEDSGEEDGEEKGEEPGEESGEEZGEITGELDGELSGELTGEMSGENAGENEGENSGENTGENUGEOSGEREGERMGERSGERTGESTGETAGETSGEUMGHATGHEEGHISGIBEGIBSGIDSGIEDGIENGIESGIFTGIGAGIGSGILAGILDGILLGILTGIMPGINGGINKGINNGINSGIOSGIPSGIRDGIRLGIRNGIROGIRRGIRTGISMGISTGITEGITSGIVEGIZZGJUSGLADGLAMGLEDGLEEGLEGGLEIGLENGLEYGLIAGLIBGLIDGLIMGLITGLOBGLOMGLOPGLOWGLUEGLUGGLUMGLUTGNARGNATGNAWGNOWGNUSGOADGOAFGOALGOASGOATGOBIGOBOGOBSGOBYGODSGOELGOERGOESGOEYGOFFGOGOGOJIGOLDGOLEGOLFGOLPGONEGONGGONKGONSGOODGOOFGOOGGOOKGOOLGOONGOOPGOORGOOSGORAGOREGORIGORMGORPGORYGOSHGOSSGOTHGOUKGOUTGOVSGOWDGOWFGOWKGOWLGOWNGOYSGRABGRADGRAMGRANGRATGRAVGRAYGREEGRENGREWGREXGREYGRIDGRIGGRIMGRINGRIPGRISGRITGROGGROKGROTGROWGRRLGRUBGRUEGRUMGUANGUARGUBSGUCKGUDEGUESGUFFGUGAGUIDGULAGULEGULFGULLGULPGULSGULYGUMPGUMSGUNGGUNKGUNSGUPSGURLGURNGURSGURUGUSHGUSTGUTSGUVSGUYSGYALGYBEGYMPGYMSGYNYGYPSGYREGYRIGYROGYTEGYVE