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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+132x^109+44x^111+306x^112+112x^114+264x^115+260x^117+4620x^118+252x^120+150x^121+22x^123+156x^124+16x^126+60x^127+6x^129+102x^130+10x^132+30x^133+12x^136+4x^138+2x^171

The gray image is a linear code over GF(3) with n=531, k=8 and d=327.
This code was found by Heurico 1.16 in 0.693 seconds.