The generator matrix

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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+312x^74+338x^75+2304x^76+1578x^77+1610x^78+3420x^79+1554x^80+1302x^81+3546x^82+1290x^83+826x^84+1080x^85+438x^86+52x^87+18x^88+12x^89+2x^90

The gray image is a linear code over GF(3) with n=360, k=9 and d=222.
This code was found by Heurico 1.16 in 0.479 seconds.