The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+15x^16+48x^17+14x^18+32x^19+16x^21+2x^26

The gray image is a linear code over GF(2) with n=72, k=7 and d=32.
This code was found by Heurico 1.16 in 0.00176 seconds.