The generator matrix
1 1 1 1 1 1 1 1 1 1 X 0 X X X X X 1
0 X 0 X 0 0 X X^2+X 0 X^2 X^2 0 0 X X^2+X X^2 0 0
0 0 X X 0 X^2+X X 0 X^2 X X X X^2+X X 0 X 0 0
0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 0 0
0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0
0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0
0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0
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+43x^12+40x^13+105x^14+120x^15+220x^16+352x^17+287x^18+352x^19+225x^20+120x^21+105x^22+40x^23+23x^24+13x^26+2x^30
The gray image is a linear code over GF(2) with n=72, k=11 and d=24.
This code was found by Heurico 1.16 in 0.0401 seconds.