The generator matrix

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

generates a code of length 42 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+82x^72+132x^74+196x^75+324x^77+512x^78+750x^80+1280x^81+2916x^82+1062x^83+2290x^84+5832x^85+1182x^86+1672x^87+708x^89+260x^90+210x^92+152x^93+6x^95+46x^96+34x^99+22x^102+2x^105+8x^108+4x^111

The gray image is a linear code over GF(3) with n=378, k=9 and d=216.
This code was found by Heurico 1.16 in 1.33 seconds.