The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2  0  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0
 0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  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+15x^16+224x^18+15x^20+1x^36

The gray image is a linear code over GF(2) with n=144, k=8 and d=64.
This code was found by Heurico 1.16 in 3.81e-009 seconds.