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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+54x^88+20x^90+2x^93+2x^96+2x^99

The gray image is a linear code over GF(3) with n=396, k=4 and d=264.
This code was found by Heurico 1.16 in 0.0196 seconds.