n=3, k0=1, k1=0
Optimal Minimum Distance: 3
Generator Matrices that generate Codes having Optimal Minimum Distance: 4,
Total No. of Codes having Optimal Minimum Distance: 1
Generator Matrices that generate Nice Codes : 1,
Total No. of Nice Codes: 1

Generator Matrix-1

a 0 0
b 0 0

Codewords:

0 0 0
b 0 0
a 0 0
c 0 0

dmin: 1
Weight Enumerator: 1x0 + 3x1 + 0x2 + 0x3
Complete Weight Enumerator: (X_0)3 + (X_0)2 (X_b)1 + (X_0)2 (X_a)1 + (X_0)2 (X_c)1

Dual Codewords:

0 0 0
0 0 a
0 0 b
0 0 c
0 a 0
0 a a
0 a b
0 a c
0 b 0
0 b a
0 b b
0 b c
0 c 0
0 c a
0 c b
0 c c

Is it a nice code?: Yes

Generator Matrix-2

a 0 a
b 0 b

Codewords:

0 0 0
b 0 b
a 0 a
c 0 c

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3
Complete Weight Enumerator: (X_0)3 + (X_0)1 (X_b)2 + (X_0)1 (X_a)2 + (X_0)1 (X_c)2

Dual Codewords:

0 0 0
0 a 0
0 b 0
0 c 0

Is it a nice code?: No

Generator Matrix-3

a a 0
b b 0

Codewords:

0 0 0
b b 0
a a 0
c c 0

dmin: 2
Weight Enumerator: 1x0 + 0x1 + 3x2 + 0x3
Complete Weight Enumerator: (X_0)3 + (X_0)1 (X_b)2 + (X_0)1 (X_a)2 + (X_0)1 (X_c)2

Dual Codewords:

0 0 0
0 0 a
0 0 b
0 0 c

Is it a nice code?: No

Generator Matrix-4

a a a
b b b

Codewords:

0 0 0
b b b
a a a
c c c

dmin: 3
Weight Enumerator: 1x0 + 0x1 + 0x2 + 3x3
Complete Weight Enumerator: (X_0)3 + (X_b)3 + (X_a)3 + (X_c)3

Dual Codewords:

0 0 0

Is it a nice code?: No