Solutions :

3-letter words (1 point): 42

CHI; EFS; EFT; EHS; ERF; ERG; EST; FEG; FEH; FEM; FER; FES; FET; FEU; GEM; GET; HEM; HER; HES; HET; HIC; HIE; HIM; ICH; MEG; MEU; MIC; REF; REG; REH; REI; REM; RUE; SEG; SET; SHE; SHH; TEF; TEG; TES; THE; URE.

4-letter words (1 point): 18

EGER; EMIC; FEHM; FEHS; FEST; GEST; GRUE; HEFT; HEST; MICH; REFS; REFT; REHS; SHET; TEFS; TEST; THEM; URGE.

5-letter words (2 points): 13

CHIEF; CHIME; EGEST; FEHME; HEFTE; HEMIC; MERGE; REGES; SEFER; THEFT; THEIC; UREIC; URGES.

6-letter words (3 points): 8

CHIEFS; CHIMER; CIERGE; EFTEST; FEHMIC; MERGES; REGEST; UREMIC.

7-letter word (7 points): 1

CIERGES.

8-letter word (11 points): 1

CHIEFEST.