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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+26x^126+48x^128+120x^129+216x^130+60x^131+1116x^132+432x^133+18x^134+70x^135+24x^137+24x^138+12x^140+16x^141+2x^144+2x^195

The gray image is a linear code over GF(3) with n=594, k=7 and d=378.
This code was found by Heurico 1.16 in 0.154 seconds.