The generator matrix

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

generates a code of length 44 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+350x^81+396x^84+426x^87+496x^90+324x^93+132x^96+42x^99+18x^108+2x^117

The gray image is a linear code over GF(3) with n=132, k=7 and d=81.
This code was found by Heurico 1.16 in 7.76 seconds.