The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 0 X 2X 2X 0 0 X X X X X X X 0 2X 0 2X 0 2X 0 X 2X X 2X 2X 0 0 2X X 0 X X X X 0 0 0 X 0 X 0 0 X X 2X 2X 0 X 2X 2X 2X X 2X 0 2X X 2X 0 2X 0 X 2X 2X 0
0 0 X 0 0 X 2X 0 2X 0 X X 2X 2X 0 X 0 X X X X 0 0 2X 2X X X 2X 0 2X 0 X X 0 2X 2X 0 X 0 2X 2X 2X X 2X 2X 0 0 2X X 0 X X X 0 2X 0 2X 2X 2X X X X 2X 2X 2X 0 2X 2X X
0 0 0 X 0 2X 2X X 0 X X 0 0 X 2X X X 2X 2X 0 0 2X 2X 2X 2X 2X X X 0 X 2X X 2X 2X X 2X X 0 0 0 X 0 X 2X 0 0 X X 0 2X 0 X X 0 2X 2X 2X 0 0 2X 2X X 2X X X 2X X 2X 0
0 0 0 0 X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 X 0 0 2X 2X X 2X X 2X 0 2X 0 0 2X 2X X 0 0 0 2X 0 X X 2X 2X X 0 X 2X X X X 0 2X X 0 X 0 X X X 0 2X 0 2X 2X 2X X X X X X
generates a code of length 69 over Z3[X]/(X^2) who´s minimum homogenous weight is 132.
Homogenous weight enumerator: w(x)=1x^0+38x^132+70x^135+540x^138+32x^141+26x^144+18x^147+2x^150+2x^207
The gray image is a linear code over GF(3) with n=207, k=6 and d=132.
This code was found by Heurico 1.16 in 0.0762 seconds.