The generator matrix

 1  0  1  1  1 X^2+X  1 X^2  1  1  1  1 X^2  1  1  X  1  1
 0  1  1 X^2+X X^2+X+1  1 X^2  1 X+1  X X^2+X X^2+1  1  0 X^2+X  X X^2+X  0
 0  0  X  0 X^2+X X^2  X  X  0 X^2+X  0 X^2  X X^2  0  X  X  0
 0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 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+47x^14+82x^15+133x^16+186x^17+167x^18+164x^19+112x^20+68x^21+37x^22+10x^23+10x^24+2x^25+5x^26

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 0.0114 seconds.