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

generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+130x^54+220x^57+374x^60+810x^63+1406x^66+1654x^69+1072x^72+526x^75+178x^78+116x^81+60x^84+8x^87+4x^90+2x^93

The gray image is a linear code over GF(3) with n=102, k=8 and d=54.
This code was found by Heurico 1.16 in 1.52 seconds.