The generator matrix

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

generates a code of length 44 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+1012x^81+1620x^82+1854x^83+4208x^84+4734x^85+4824x^86+7074x^87+7290x^88+6318x^89+7316x^90+5562x^91+2898x^92+2600x^93+1206x^94+144x^95+288x^96+86x^99+14x^102

The gray image is a linear code over GF(3) with n=396, k=10 and d=243.
This code was found by Heurico 1.16 in 70.7 seconds.