The generator matrix

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

generates a code of length 31 over Z3[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+78x^48+218x^51+246x^54+240x^57+1720x^60+13122x^62+3158x^63+316x^66+244x^69+184x^72+118x^75+32x^78+4x^84+2x^90

The gray image is a linear code over GF(3) with n=279, k=9 and d=144.
This code was found by Heurico 1.16 in 1.23 seconds.