The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+144x^24+90x^25+1638x^26+1448x^27+5004x^28+7992x^29+19392x^30+20088x^31+50760x^32+37080x^33+19782x^34+10836x^35+2322x^36+234x^37+216x^38+120x^39

The gray image is a linear code over GF(3) with n=144, k=11 and d=72.
This code was found by Heurico 1.16 in 10.4 seconds.