The generator matrix

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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+456x^77+366x^78+558x^80+228x^81+432x^83+128x^84+12x^86+2x^90+4x^93

The gray image is a linear code over GF(3) with n=360, k=7 and d=231.
This code was found by Heurico 1.16 in 0.165 seconds.