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 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 2X 2X 0 2X X X 0 0 X X 2X 2X 0 X 2X 0 X 2X 2X 0 0 2X 0 X 2X 2X X 2X X 0 X 0 X 2X 2X 2X 0 0 X X 0 X 2X 2X 2X 0 0 0 0 X X 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 2X 0 2X X X 0 2X 2X 2X 0 X 0 2X 0 2X 2X 2X 0 2X 0 0 2X 2X 0 0 2X 2X 0 X 0 2X 2X 0 0 X 2X X X X X X X X X X 0 0 0 X 2X X 0
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 0 2X 0 2X 2X X 0 X 2X 2X 0 0 2X 0 2X 0 X 0 2X 0 2X 2X 0 X X X X X X X 2X X 0 X 0 2X 2X X 0 0 0 X 2X 2X X 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 2X 0 X X X X 0 2X X 0 0 2X 2X 0 2X X X X 2X 0 0 2X 2X 0 X X X X X X X X X X X X X 0 0 X 0 2X 2X 2X 0 X 2X 2X 2X X 0
generates a code of length 88 over Z3[X]/(X^2) who´s minimum homogenous weight is 168.
Homogenous weight enumerator: w(x)=1x^0+20x^168+30x^171+50x^174+486x^176+70x^177+50x^180+20x^183+2x^264
The gray image is a linear code over GF(3) with n=264, k=6 and d=168.
This code was found by Heurico 1.16 in 0.109 seconds.