The generator matrix

 1  0  0  1  1  1  0  X  1  X  1  1  1  0  X X^2  0  X
 0  1  0  1  0  1  1 X^2 X^2+1  1 X^2+X  0 X+1  1  X  1  1  1
 0  0  1  1  1  X  1  1 X+1  0 X^2 X+1  X X+1  1  0 X^2+1  1
 0  0  0  X X^2  0 X^2  0 X^2 X^2+X  X X^2+X  X  X X^2 X^2  0  X

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+52x^14+228x^15+269x^16+268x^17+394x^18+336x^19+248x^20+176x^21+48x^22+12x^23+10x^24+4x^25+2x^26

The gray image is a linear code over GF(2) with n=72, k=11 and d=28.
This code was found by Heurico 1.11 in 0.016 seconds.