The generator matrix

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

generates a code of length 54 over Z3[X]/(X^3) who´s minimum homogenous weight is 97.

Homogenous weight enumerator: w(x)=1x^0+576x^97+1218x^98+3558x^99+6204x^100+9948x^101+13902x^102+21432x^103+27540x^104+37066x^105+46896x^106+55440x^107+58096x^108+64158x^109+57582x^110+46466x^111+36456x^112+21858x^113+12096x^114+6246x^115+2742x^116+1462x^117+162x^118+78x^119+94x^120+108x^121+12x^122+32x^123+12x^124

The gray image is a linear code over GF(3) with n=486, k=12 and d=291.
This code was found by Heurico 1.16 in 419 seconds.