The generator matrix

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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+630x^105+1722x^106+3906x^107+7030x^108+11832x^109+15114x^110+19274x^111+29370x^112+36948x^113+44514x^114+55734x^115+58146x^116+56570x^117+56964x^118+47286x^119+34460x^120+25920x^121+13530x^122+6636x^123+3444x^124+1416x^125+656x^126+126x^127+60x^128+50x^129+42x^130+12x^131+24x^132+12x^133+12x^135

The gray image is a linear code over GF(3) with n=522, k=12 and d=315.
This code was found by Heurico 1.16 in 456 seconds.