The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+1050x^126+1476x^127+2538x^128+5148x^129+5706x^130+6444x^131+12060x^132+11484x^133+13752x^134+18242x^135+17226x^136+16038x^137+18354x^138+15030x^139+10836x^140+10086x^141+5526x^142+2718x^143+2124x^144+414x^145+162x^146+504x^147+156x^150+48x^153+24x^156

The gray image is a linear code over GF(3) with n=612, k=11 and d=378.
This code was found by Heurico 1.16 in 72.6 seconds.