The generator matrix
1 0 1 1 1 X^2 1 1 0 1 1 1 1 1 1 1 1 1
0 1 1 0 X+1 1 X+1 0 1 X^2+1 X^2+X+1 X^2+1 X X^2+1 X^2+X X^2+X+1 1 0
0 0 X 0 0 X^2 X X^2+X X^2+X X^2 X^2 X X 0 X 0 X^2+X 0
0 0 0 X X^2 X X X^2+X X X^2 X X X^2 X^2+X X^2+X X 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+36x^14+96x^15+126x^16+166x^17+200x^18+164x^19+106x^20+72x^21+33x^22+12x^23+7x^24+2x^25+2x^26+1x^30
The gray image is a linear code over GF(2) with n=72, k=10 and d=28.
This code was found by Heurico 1.16 in 0.0113 seconds.