The generator matrix

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

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+204x^12+504x^14+128x^15+1217x^16+896x^17+2224x^18+896x^19+1368x^20+128x^21+440x^22+150x^24+32x^26+4x^28

The gray image is a linear code over GF(2) with n=72, k=13 and d=24.
This code was found by Heurico 1.16 in 2.85 seconds.