The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+144x^44+114x^45+144x^47+54x^48+108x^50+36x^51+72x^53+20x^54+18x^56+18x^57

The gray image is a linear code over GF(3) with n=72, k=6 and d=44.
This code was found by Heurico 1.13 in 0.00257 seconds.