The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who�s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+28x^39+82x^42+162x^44+46x^45+1458x^46+324x^47+32x^48+32x^54+10x^57+8x^60+2x^63+2x^66

The gray image is a linear code over GF(3) with n=207, k=7 and d=117.
This code was found by Heurico 1.16 in 0.0144 seconds.