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

generates a code of length 38 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+54x^75+162x^76+12x^78+6x^81+6x^84+2x^90

The gray image is a linear code over GF(3) with n=342, k=5 and d=225.
This code was found by Heurico 1.16 in 0.0141 seconds.