The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+264x^37+360x^38+638x^39+1272x^40+1452x^41+1802x^42+2544x^43+2724x^44+4016x^45+5040x^46+4656x^47+6130x^48+6840x^49+4800x^50+4954x^51+4314x^52+2820x^53+1866x^54+1392x^55+636x^56+252x^57+204x^58+48x^59+12x^60+12x^63

The gray image is a linear code over GF(3) with n=72, k=10 and d=37.
This code was found by Heurico 1.16 in 12.7 seconds.