The generator matrix

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

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+612x^112+1236x^113+1594x^114+2148x^115+2142x^116+1718x^117+2094x^118+1434x^119+1504x^120+1578x^121+1284x^122+762x^123+810x^124+534x^125+168x^126+30x^127+6x^128+2x^129+6x^130+2x^132+12x^133+6x^134

The gray image is a linear code over GF(3) with n=531, k=9 and d=336.
This code was found by Heurico 1.16 in 0.756 seconds.