The generator matrix

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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+546x^101+1328x^102+3816x^103+6444x^104+11156x^105+14742x^106+21012x^107+27446x^108+37836x^109+46092x^110+52810x^111+59214x^112+60306x^113+58608x^114+46464x^115+35976x^116+22080x^117+13812x^118+6600x^119+3090x^120+1386x^121+336x^122+88x^123+84x^124+72x^125+48x^126+30x^127+6x^128+6x^129+6x^130

The gray image is a linear code over GF(3) with n=504, k=12 and d=303.
This code was found by Heurico 1.16 in 438 seconds.