The generator matrix

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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+414x^113+894x^114+252x^115+966x^116+774x^117+342x^118+696x^119+816x^120+180x^121+516x^122+480x^123+36x^124+132x^125+2x^126+24x^128+16x^129+6x^131+6x^132+8x^138

The gray image is a linear code over GF(3) with n=531, k=8 and d=339.
This code was found by Heurico 1.16 in 11.7 seconds.