The generator matrix

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

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+50x^14+128x^15+279x^16+376x^17+384x^18+408x^19+252x^20+104x^21+42x^22+8x^23+12x^24+4x^26

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 0.016 seconds.