The generator matrix

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

generates a code of length 29 over Z3[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+128x^54+72x^55+102x^56+132x^57+48x^58+24x^59+64x^60+24x^61+24x^62+40x^63+6x^64+12x^65+30x^66+12x^67+6x^69+2x^72+2x^78

The gray image is a linear code over GF(3) with n=87, k=6 and d=54.
This code was found by Heurico 1.16 in 0.00948 seconds.