The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 128.

Homogenous weight enumerator: w(x)=1x^0+852x^128+1536x^129+1998x^130+3210x^131+4574x^132+4050x^133+5442x^134+5802x^135+4644x^136+5880x^137+5622x^138+3888x^139+3936x^140+3116x^141+1674x^142+1338x^143+898x^144+270x^145+144x^146+42x^147+72x^149+32x^150+24x^152+4x^153

The gray image is a linear code over GF(3) with n=612, k=10 and d=384.
This code was found by Heurico 1.16 in 29.4 seconds.