The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+48x^13+106x^14+136x^15+182x^16+328x^17+464x^18+336x^19+159x^20+128x^21+98x^22+40x^23+9x^24+8x^25+4x^26+1x^28

The gray image is a linear code over GF(2) with n=72, k=11 and d=26.
This code was found by Heurico 1.16 in 0.0644 seconds.