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  X  0  1  1
 0  X  0 X^2 2X 2X^2+X  X 2X^2+2X 2X X^2 2X^2+X 2X^2+2X 2X^2 2X^2 2X 2X^2+2X 2X^2+X  X X^2+2X X^2+2X 2X^2 2X^2 X^2+2X 2X^2+X  X  0 X^2+X X^2+X X^2 2X 2X^2+2X 2X^2+X X^2+2X X^2  0  X  0 X^2+X 2X^2+2X  0 X^2+X 2X^2+2X  0 2X^2+X  X 2X X^2+2X 2X^2 2X^2 2X^2 X^2+2X X^2+X X^2+X X^2 2X^2+X X^2 X^2+X X^2 2X 2X^2+X X^2+2X 2X^2+2X  X X^2  X  0 2X X^2+X
 0  0  X 2X^2+2X X^2 2X^2+2X  X 2X^2+X X^2+2X X^2 2X^2+X 2X  X X^2+2X 2X^2+2X 2X^2 2X 2X^2 2X^2+X 2X 2X^2+X 2X^2+2X 2X^2 2X^2 2X X^2  X 2X^2+2X  0  0 X^2+X X^2  X 2X^2+X 2X X^2+X X^2+2X 2X^2+X  X 2X^2 X^2+2X X^2+2X X^2+X  0 X^2 2X X^2+X X^2 X^2+X 2X X^2+2X X^2+X 2X X^2+2X  X 2X^2 X^2  X X^2+X X^2+2X  0 X^2 X^2+2X X^2+X  X  X 2X^2+X 2X^2+2X

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 132.

Homogenous weight enumerator: w(x)=1x^0+102x^132+78x^133+318x^134+254x^135+684x^136+456x^137+150x^138+24x^139+24x^140+30x^141+18x^142+12x^143+28x^144+6x^145+2x^198

The gray image is a linear code over GF(3) with n=612, k=7 and d=396.
This code was found by Heurico 1.16 in 0.131 seconds.