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  X  X  1  1  1  X  1  1  X  X  X  1  1  1  1  1  1  X  X  X  1  X  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0 2X  X 2X  X  X 2X  0  X  0  0 2X 2X  0 2X  X  0  0  X  X  X 2X  X 2X  0  X  X  X 2X  X 2X 2X  X  X  X  X  0  0  0  X 2X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X 2X 2X  0 2X  X  0 2X  0 2X  0  X  X  X  0  X 2X  X  X  0 2X  X  X  0 2X 2X 2X  X  X  X  X  0 2X  X 2X  X  0 2X 2X 2X 2X  X  X  0
 0  0  0  X  0  0  0  0  0  X  X 2X 2X 2X  0 2X  0  0  X 2X 2X 2X  X  X 2X  0  X  0 2X  X  X  0  0  0 2X  0 2X 2X  X  0  0  X 2X  X  0 2X 2X 2X  0 2X 2X  X  0  0 2X 2X 2X
 0  0  0  0  X  0  0  0  X 2X 2X 2X  X  X 2X 2X  X  0  X  X 2X 2X  X 2X 2X 2X  X 2X  X 2X  0 2X 2X 2X 2X  X 2X  0 2X  0  0 2X  X  0 2X  0  X  0  X 2X  0  0  0  0  0 2X  0
 0  0  0  0  0  X  0  0 2X 2X  X  X  0 2X  0  X  X 2X  X  0  0 2X  X 2X 2X  X 2X  X  0 2X 2X  0  0  X  X  0  X  0  0 2X  X  0  X  0  0 2X  0  0  0 2X  0 2X  X  0 2X 2X  0
 0  0  0  0  0  0  X  0 2X  X 2X  X 2X  0  0  0  0  X 2X 2X  0  0 2X  0 2X 2X  X  X  X 2X 2X 2X 2X  0  0  X  X  0 2X  0  0  X 2X  0  X  X  0  0  0 2X 2X 2X  0 2X  0 2X  0
 0  0  0  0  0  0  0  X  X  0  X  0  X  0 2X 2X 2X 2X  0 2X  0  0 2X 2X  X  0 2X  X  0 2X  X  0  X  0  X  0 2X  X  X  X  X  X 2X  0  0  X  0 2X 2X 2X  0 2X 2X 2X  0 2X 2X

generates a code of length 57 over Z3[X]/(X^2) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+110x^93+270x^96+406x^99+30x^100+472x^102+288x^103+506x^105+672x^106+562x^108+1740x^109+620x^111+3060x^112+612x^114+3480x^115+636x^117+2442x^118+652x^120+1188x^121+590x^123+222x^124+418x^126+304x^129+216x^132+108x^135+54x^138+20x^141+2x^144+2x^147

The gray image is a linear code over GF(3) with n=171, k=9 and d=93.
This code was found by Heurico 1.16 in 9.91 seconds.