The generator matrix

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

generates a code of length 20 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+80x^24+188x^27+356x^30+642x^33+926x^36+1202x^39+13122x^40+1232x^42+926x^45+632x^48+258x^51+92x^54+24x^57+2x^60

The gray image is a linear code over GF(3) with n=60, k=9 and d=24.
This code was found by Heurico 1.16 in 1.25 seconds.