The generator matrix

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

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+197x^16+128x^17+400x^18+128x^19+144x^20+16x^22+10x^24

The gray image is a linear code over GF(2) with n=144, k=10 and d=64.
This code was found by Heurico 1.16 in 6.87e-008 seconds.