The generator matrix

 1  1  1  1  1  1  1  X  1  0  1  1  1  1  X  1  1 X^2
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^2+X X^3+X  X  0 X^3+X^2 X^3+X  0 X^3+X X^2+X X^2+X X^3+X^2
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3
 0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3
 0  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 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+51x^14+48x^15+293x^16+272x^17+733x^18+272x^19+274x^20+48x^21+45x^22+6x^24+3x^26+2x^28

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 0.015 seconds.