The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X X^2  1  1  1  1  X
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3  0  0  0 X^3 X^2 X^3+X^2 X^2 X^3+X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^2
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  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+87x^14+16x^15+185x^16+368x^17+752x^18+368x^19+173x^20+16x^21+55x^22+24x^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.