The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  1  1
 0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2  0 X^3 X^2  0 X^2 X^3  0  0
 0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  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+7x^16+110x^18+8x^20+2x^26

The gray image is a linear code over GF(2) with n=144, k=7 and d=64.
This code was found by Heurico 1.16 in 3.81e-009 seconds.