The generator matrix

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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+288x^112+216x^113+526x^114+846x^115+648x^116+372x^117+708x^118+648x^119+534x^120+738x^121+432x^122+244x^123+324x^124+10x^126+12x^127+6x^129+4x^132+2x^135+2x^153

The gray image is a linear code over GF(3) with n=531, k=8 and d=336.
This code was found by Heurico 1.16 in 0.873 seconds.