The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+32x^21+18x^22+138x^24+180x^25+162x^26+308x^27+720x^28+972x^29+16518x^30+1440x^31+1944x^32+32628x^33+1440x^34+1296x^35+468x^36+576x^37+186x^39+12x^42+6x^45+4x^48

The gray image is a linear code over GF(3) with n=144, k=10 and d=63.
This code was found by Heurico 1.16 in 1.16 seconds.