The generator matrix

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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+104x^69+192x^70+506x^72+594x^73+810x^74+2444x^75+1932x^76+4860x^77+6858x^78+4356x^79+9720x^80+9112x^81+4380x^82+6480x^83+4694x^84+1362x^85+194x^87+258x^88+56x^90+48x^91+38x^93+24x^96+18x^99+6x^102+2x^105

The gray image is a linear code over GF(3) with n=360, k=10 and d=207.
This code was found by Heurico 1.16 in 6.35 seconds.