The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+6x^28+12x^29+38x^30+12x^31+6x^32+2x^33+4x^36

The gray image is a linear code over GF(3) with n=45, k=4 and d=28.
This code was found by Heurico 1.16 in 0.000365 seconds.