The generator matrix

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

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+72x^105+18x^106+150x^107+182x^108+486x^109+762x^110+514x^111+2106x^112+2058x^113+1012x^114+7740x^115+4386x^116+1774x^117+12960x^118+5718x^119+1752x^120+9882x^121+3486x^122+890x^123+1800x^124+756x^125+164x^126+162x^128+100x^129+18x^131+38x^132+14x^135+18x^138+4x^141+16x^144+10x^147

The gray image is a linear code over GF(3) with n=531, k=10 and d=315.
This code was found by Heurico 1.16 in 8.81 seconds.