The generator matrix

 1  1  1  1  1  1  1  1  0  1 X^3  1  1  1  1  X  1  X
 0  X  0  X X^3  0 X^3+X  X  X X^2  X X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X^2  X X^2+X X^3+X^2+X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^3 X^2 X^3+X  X  0 X^3+X^2+X  X  X X^3+X^2+X X^3+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+222x^16+128x^17+352x^18+128x^19+167x^20+16x^22+9x^24+1x^28

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 0.015 seconds.