The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  0  1  1  1  1  1  X  X  X  1  1  1  1  1  1  1  1  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X X^2 2X^2+X 2X X^2+2X  0 2X^2+X X^2+X X^2+2X X^2 2X  0 2X^2+X X^2+X  0 2X X^2+2X  X  0 X^2+2X 2X^2+X 2X^2 X^2+X X^2+2X 2X^2+2X X^2+X X^2 2X^2+X X^2+X 2X^2 2X 2X^2+X 2X  X X^2+2X X^2+X X^2+X X^2+2X  X 2X^2+X 2X 2X^2+X 2X^2 X^2+X 2X^2 2X^2  X 2X  0 X^2 2X^2
 0  0 X^2  0  0  0  0 2X^2 X^2  0 X^2 2X^2 2X^2  0  0 X^2  0  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 X^2  0 X^2 2X^2  0 2X^2 2X^2  0  0 2X^2  0 2X^2 X^2 2X^2 X^2  0 X^2 X^2 2X^2 2X^2  0  0 2X^2 2X^2 2X^2 X^2 X^2 X^2
 0  0  0 X^2  0  0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2  0 2X^2 2X^2  0 X^2 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2  0  0 X^2 X^2 X^2 2X^2 2X^2  0  0 2X^2  0 X^2  0 2X^2  0  0 2X^2 X^2 2X^2 2X^2  0  0 X^2 X^2  0
 0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2  0 X^2 2X^2  0 2X^2  0 2X^2  0 2X^2 2X^2  0  0 2X^2 X^2  0  0 2X^2 2X^2 2X^2 2X^2 2X^2  0  0 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 X^2  0 X^2  0 2X^2 X^2 X^2  0  0 2X^2 2X^2  0 2X^2 X^2 X^2 X^2  0 2X^2 X^2
 0  0  0  0  0 X^2 X^2  0 2X^2 X^2  0  0 X^2 X^2 2X^2 2X^2 X^2 X^2  0 2X^2  0  0 2X^2 X^2 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 X^2  0 X^2  0 2X^2 2X^2 X^2 X^2  0 X^2 2X^2 2X^2 X^2  0  0  0  0 2X^2  0  0 2X^2 2X^2  0  0 X^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+52x^105+42x^106+144x^107+96x^108+156x^109+384x^110+108x^111+492x^112+336x^113+586x^114+1506x^115+1902x^116+2012x^117+2676x^118+3450x^119+2016x^120+1950x^121+522x^122+54x^123+282x^124+378x^125+54x^126+138x^127+108x^128+34x^129+42x^130+60x^131+20x^132+6x^133+6x^134+34x^135+16x^138+4x^141+6x^144+4x^147+2x^150+2x^153+2x^159

The gray image is a linear code over GF(3) with n=531, k=9 and d=315.
This code was found by Heurico 1.16 in 2.06 seconds.