The generator matrix

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

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+188x^14+364x^15+467x^16+684x^17+708x^18+640x^19+532x^20+336x^21+140x^22+20x^23+8x^24+4x^25+4x^26

The gray image is a linear code over GF(2) with n=72, k=12 and d=28.
This code was found by Heurico 1.11 in 0.047 seconds.