The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+156x^82+126x^83+564x^84+750x^85+216x^86+974x^87+1218x^88+132x^89+1112x^90+870x^91+108x^92+150x^93+60x^94+54x^95+28x^96+24x^97+12x^98+6x^108

The gray image is a linear code over GF(3) with n=396, k=8 and d=246.
This code was found by Heurico 1.16 in 0.1 seconds.