The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  1  1
 0 X^3  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3
 0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3
 0  0  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3
 0  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 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0
 0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 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+33x^14+45x^16+96x^17+768x^18+32x^21+30x^22+18x^24+1x^30

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 0.016 seconds.