The generator matrix

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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+66x^76+2x^78+6x^79+4x^84+2x^87

The gray image is a linear code over GF(3) with n=342, k=4 and d=228.
This code was found by Heurico 1.16 in 0.0113 seconds.