The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0  0  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2  0 X^3+X^2
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3
 0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  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+36x^14+66x^16+64x^17+704x^18+64x^19+48x^20+28x^22+12x^24+1x^32

The gray image is a linear code over GF(2) with n=144, k=10 and d=56.
This code was found by Heurico 1.16 in 0.015 seconds.