The generator matrix

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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+456x^101+598x^102+1062x^103+1302x^104+1140x^105+1764x^106+2196x^107+1570x^108+3024x^109+2418x^110+1332x^111+1422x^112+690x^113+396x^114+18x^115+120x^116+38x^117+60x^119+12x^120+42x^122+12x^123+6x^125+2x^126+2x^129

The gray image is a linear code over GF(3) with n=486, k=9 and d=303.
This code was found by Heurico 1.16 in 57.3 seconds.