The generator matrix

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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+40x^96+126x^98+160x^99+108x^100+510x^101+474x^102+864x^103+1206x^104+2452x^105+2916x^106+3600x^107+6848x^108+5400x^109+6138x^110+9006x^111+5616x^112+4152x^113+4652x^114+2592x^115+1452x^116+198x^117+264x^119+110x^120+42x^122+24x^123+6x^125+44x^126+20x^129+12x^132+12x^135+2x^138+2x^141

The gray image is a linear code over GF(3) with n=495, k=10 and d=288.
This code was found by Heurico 1.16 in 7.98 seconds.