The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1
 0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2
 0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0 X^2  0  0 X^2  0 X^2  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  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 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+19x^12+66x^14+32x^15+45x^16+96x^17+512x^18+96x^19+42x^20+32x^21+60x^22+18x^24+3x^28+2x^30

The gray image is a linear code over GF(2) with n=72, k=10 and d=24.
This code was found by Heurico 1.16 in 0.0125 seconds.