The generator matrix

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

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+254x^84+176x^87+148x^90+104x^93+40x^96+4x^108+2x^120

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 0.07 seconds.