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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 99.

Homogenous weight enumerator: w(x)=1x^0+50x^99+18x^100+180x^101+290x^102+108x^103+474x^104+1406x^105+1080x^106+1488x^107+4576x^108+3960x^109+3414x^110+8800x^111+6534x^112+4302x^113+9586x^114+5076x^115+2544x^116+3182x^117+720x^118+564x^119+374x^120+138x^122+62x^123+18x^125+36x^126+36x^129+12x^132+12x^135+4x^138+4x^141

The gray image is a linear code over GF(3) with n=504, k=10 and d=297.
This code was found by Heurico 1.16 in 8.24 seconds.