The generator matrix

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

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+116x^12+190x^14+128x^15+575x^16+384x^17+1286x^18+384x^19+614x^20+128x^21+186x^22+96x^24+2x^26+6x^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 0.156 seconds.