The generator matrix

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

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+24x^14+98x^15+242x^16+416x^17+514x^18+420x^19+199x^20+80x^21+36x^22+10x^23+5x^24+2x^26+1x^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 0.031 seconds.