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

generates a code of length 32 over Z3[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+20x^60+20x^63+162x^64+30x^66+8x^69+2x^96

The gray image is a linear code over GF(3) with n=96, k=5 and d=60.
This code was found by Heurico 1.16 in 0.0048 seconds.