The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^2 X^3+X X^3+X X^3  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0  0
 0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0

generates a code of length 18 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+27x^16+272x^17+19x^18+128x^19+4x^20+48x^21+12x^22+1x^34

The gray image is a linear code over GF(2) with n=144, k=9 and d=64.
This code was found by Heurico 1.16 in -3.24e-008 seconds.