The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+40x^12+96x^13+172x^14+228x^15+398x^16+692x^17+814x^18+712x^19+443x^20+232x^21+128x^22+84x^23+41x^24+4x^25+6x^26+5x^28

The gray image is a linear code over GF(2) with n=72, k=12 and d=24.
This code was found by Heurico 1.16 in 0.155 seconds.