The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  1  1
 0  X  0  0  0  0  X 2X 2X  0  0  X  X  X  X  X  X  X  0 2X  0 2X  0 2X  0  X  X 2X  X  0  X  0 2X 2X  X  0 2X  X  0  X 2X  0  0  X
 0  0  X  0  0  X 2X  0 2X  0  X  X 2X 2X  0  X  0  X  X  X  X  0  0 2X 2X  X 2X  0  X 2X 2X  0  0 2X  0 2X  0  X 2X  X  X 2X  0 2X
 0  0  0  X  0 2X 2X  X  0  X  X  0  0  X 2X  X  X 2X 2X  0  0 2X 2X 2X 2X 2X  0  0  X  X  X  X  0 2X  0  X 2X 2X  0 2X  0  0 2X 2X
 0  0  0  0  X 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  X  0  0 2X 2X  X 2X  X 2X 2X  0  0  0  X  X  X  X  X  X  X  0  0  X 2X 2X 2X  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+38x^81+136x^84+254x^87+242x^90+16x^93+8x^96+12x^99+10x^102+8x^105+2x^108+2x^126

The gray image is a linear code over GF(3) with n=132, k=6 and d=81.
This code was found by Heurico 1.16 in 0.0181 seconds.