The generator matrix

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

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+270x^16+512x^18+224x^20+16x^24+1x^32

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 1.61 seconds.