The generator matrix
1 0 1 1 1 X^2+X 1 1 0 1 1 0 1 1 1 1 X 1
0 1 X+1 X^2+X 1 1 0 X+1 1 0 X+1 1 X^2+X X^2 0 X^2+X X^2+X 0
0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0
0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0
0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 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 14.
Homogenous weight enumerator: w(x)=1x^0+24x^14+32x^15+64x^16+96x^17+82x^18+96x^19+60x^20+32x^21+20x^22+2x^24+2x^26+1x^32
The gray image is a linear code over GF(2) with n=72, k=9 and d=28.
This code was found by Heurico 1.16 in 0.00396 seconds.