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
 0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X 2X 2X  0  0
 0  0  X  0  0  0  0  0  0  0  X 2X 2X 2X  X  0  X  0  X  0  0  0
 0  0  0  X  0  0  0  0  0  X 2X  0 2X 2X  X  X 2X  0 2X  0  X  0
 0  0  0  0  X  0  0  0  0 2X 2X  0 2X  0 2X  0  X 2X 2X 2X 2X  0
 0  0  0  0  0  X  0  0  0 2X 2X  X  X  0 2X  X  X  X  0  0  X  0
 0  0  0  0  0  0  X  0  0 2X 2X 2X  0  X  X  0  X 2X  0  0  X  0
 0  0  0  0  0  0  0  X  0 2X  X 2X  0 2X  0  X  0  0  0 2X 2X  0
 0  0  0  0  0  0  0  0  X 2X  0 2X 2X  X  0 2X  X 2X  X 2X  0  0

generates a code of length 22 over Z3[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+56x^24+302x^27+490x^30+924x^33+1566x^36+2452x^39+3318x^42+39366x^44+3342x^45+2970x^48+2140x^51+1308x^54+566x^57+204x^60+42x^63+2x^66

The gray image is a linear code over GF(3) with n=66, k=10 and d=24.
This code was found by Heurico 1.16 in 9.23 seconds.