The generator matrix

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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+90x^101+120x^102+414x^103+840x^104+422x^105+1050x^106+2016x^107+786x^108+2160x^109+3438x^110+1072x^111+2400x^112+2802x^113+634x^114+648x^115+468x^116+96x^117+90x^118+36x^119+12x^120+30x^121+30x^122+12x^124+4x^126+2x^129+6x^132+2x^135+2x^144

The gray image is a linear code over GF(3) with n=495, k=9 and d=303.
This code was found by Heurico 1.16 in 0.981 seconds.