The generator matrix

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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+210x^102+102x^103+288x^104+506x^105+516x^106+510x^107+864x^108+1554x^109+2070x^110+1276x^111+2850x^112+3342x^113+1188x^114+1908x^115+822x^116+494x^117+186x^118+108x^119+314x^120+90x^121+114x^122+160x^123+78x^124+36x^125+68x^126+6x^127+18x^129+2x^135+2x^144

The gray image is a linear code over GF(3) with n=504, k=9 and d=306.
This code was found by Heurico 1.16 in 1.73 seconds.