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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+254x^114+464x^117+972x^118+378x^120+68x^123+46x^126+2x^132+2x^171

The gray image is a linear code over GF(3) with n=531, k=7 and d=342.
This code was found by Heurico 1.16 in 0.223 seconds.