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

generates a code of length 67 over Z3[X]/(X^3) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+198x^127+342x^128+112x^129+396x^130+516x^131+518x^132+810x^133+810x^134+906x^135+786x^136+552x^137+138x^138+90x^139+84x^140+22x^141+54x^142+36x^143+36x^145+78x^146+2x^147+36x^148+12x^149+18x^151+6x^154+2x^180

The gray image is a linear code over GF(3) with n=603, k=8 and d=381.
This code was found by Heurico 1.16 in 3.23 seconds.