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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+90x^115+144x^116+8x^117+90x^118+288x^119+12x^120+90x^121+4x^123+2x^159

The gray image is a linear code over GF(3) with n=531, k=6 and d=345.
This code was found by Heurico 1.16 in 0.0831 seconds.