The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+210x^84+282x^87+118x^90+54x^93+24x^96+16x^99+24x^102

The gray image is a linear code over GF(3) with n=132, k=6 and d=84.
This code was found by Heurico 1.16 in 0.0164 seconds.