The generator matrix

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

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+220x^54+156x^55+114x^56+632x^57+852x^58+480x^59+1290x^60+2214x^61+1278x^62+2628x^63+4116x^64+2724x^65+3960x^66+6396x^67+3558x^68+4686x^69+6588x^70+3096x^71+3504x^72+4152x^73+1536x^74+1938x^75+1500x^76+336x^77+600x^78+270x^79+148x^81+58x^84+12x^87+6x^90

The gray image is a linear code over GF(3) with n=102, k=10 and d=54.
This code was found by Heurico 1.16 in 78.8 seconds.