The generator matrix

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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+724x^126+1836x^127+1836x^128+3180x^129+4500x^130+3978x^131+5308x^132+6018x^133+4950x^134+5504x^135+5598x^136+3996x^137+3934x^138+3354x^139+1638x^140+1400x^141+930x^142+126x^143+84x^144+72x^145+14x^147+48x^148+6x^150+12x^153+2x^162

The gray image is a linear code over GF(3) with n=603, k=10 and d=378.
This code was found by Heurico 1.16 in 12.9 seconds.