The generator matrix

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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+546x^73+1692x^74+2474x^75+3132x^76+4140x^77+6188x^78+6726x^79+6360x^80+9792x^81+5934x^82+5076x^83+3552x^84+1992x^85+1152x^86+92x^87+96x^88+48x^89+8x^90+36x^91+4x^93+6x^94+2x^105

The gray image is a linear code over GF(3) with n=360, k=10 and d=219.
This code was found by Heurico 1.16 in 12.7 seconds.