I found this in the AISC Histroic Shapes Database. It's called an H3 but the weight matches. The H6's were either too heavy or too light.
Library: HISTORIC
Type: H
ID = 639
Designation = H3
W = 24.1
A = 7.01
D = 6
TW = 0.313
BF = 6
TF = 0.451
T = 4.268
K = 0.866
BF_2TF = 6.65
H_TW = 13.6
FY3P = -
X1 = 4974
X2 = 225
IX = 45.1
ZX = 17
SX = 15
RX = 2.54
IY = 14.7
ZY = 7.8
SY = 4.9
RY = 1.45
J = 0.5
CW = 113
a = 24.3
WNO = 8.32
SW = 5.63
QF = 3.56
QW = 8.52
FSTR = C 1921,C 1923,C 1926,