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  6  1
 0  X  0  0 2X X+6 2X+6  X 2X X+6  6  0 X+6 2X+6  3 2X+6 2X+6 X+3  3 X+3 X+6  6 2X  6 2X+3 2X X+6 2X+3  0 2X 2X+6  3 X+6 2X+3  X  X  X  0 2X+6 X+3 X+6  X 2X+3 2X+3 X+6  X  0  0 X+6  3  X  3  6 2X+3  X  X
 0  0  X 2X  0 2X+3 X+3  X 2X+3 2X+6  X  6 X+3 X+3 2X  0 2X+6  3  0  X 2X X+6 2X+3  X  6 2X+6  0 X+3 2X+6 X+6 2X 2X+6  3  6 2X 2X+6 2X  X  0  6  6 2X+6  X  3 X+3 2X+6  6 X+3 2X+3  X 2X+3  X 2X X+3  X  X
 0  0  0  3  0  0  6  0  0  3  6  3  6  3  6  3  6  6  6  3  6  0  6  6  0  3  3  3  0  0  0  6  0  3  0  6  6  3  3  3  6  0  0  6  0  3  0  3  3  6  6  3  3  3  3  0
 0  0  0  0  3  6  0  3  6  0  6  3  0  0  0  3  6  0  3  3  0  3  0  3  6  6  6  3  6  3  3  6  6  6  0  6  3  0  0  3  6  3  0  3  0  6  6  6  6  3  0  0  0  6  0  6

generates a code of length 56 over Z9[X]/(X^2+6,3X) 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 code over GF(3) with n=504, k=9 and d=306.
This code was found by Heurico 1.16 in 1.74 seconds.