The generator matrix

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

generates a code of length 18 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+80x^14+142x^16+512x^17+608x^18+512x^19+96x^20+80x^22+16x^24+1x^32

The gray image is a linear code over GF(2) with n=144, k=11 and d=56.
This code was found by Heurico 1.16 in 0.047 seconds.