The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  0  1  1 X^2  1  X
 0  X  0  0  0  X  0  0  0 X^2  X  X  0 X^2+X  X X^2  X  X
 0  0  X  0  0  X  0  X X^2+X X^2+X X^2+X X^2  X X^2+X X^2  X X^2+X  0
 0  0  0  X  0  X  X  X  X  0 X^2 X^2+X  0 X^2+X  X X^2+X X^2+X  0
 0  0  0  0  X  X  X X^2  X  X  0  0 X^2 X^2 X^2+X X^2  X  X
 0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 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+199x^12+494x^14+128x^15+1290x^16+896x^17+2138x^18+896x^19+1366x^20+128x^21+482x^22+148x^24+22x^26+3x^28+1x^32

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 0.835 seconds.