The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0  1  1  0
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1  0 X+1  1
 0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2
 0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 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+126x^12+336x^14+2049x^16+3168x^18+2049x^20+336x^22+126x^24+1x^36

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 17.1 seconds.