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 2X^2+2X  1  1  X 2X^2+X  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 X^2+2X+1 2X^2+X+1  1 2X^2+X+2  2  1  1 X^2
 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 X^2+2X  0 X^2 2X^2 2X 2X^2+X 2X 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+492x^113+732x^114+468x^115+840x^116+672x^117+432x^118+720x^119+666x^120+324x^121+546x^122+408x^123+72x^124+132x^125+14x^126+12x^128+10x^129+6x^131+6x^132+6x^137+2x^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 15.3 seconds.