The generator matrix

 1  1  1  1  1  1  1  1  X  1  1 X^2  1  1 X^2  X  X  X
 0 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2  0 X^3  0 X^3  0 X^2 X^2 X^3+X^2 X^3
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3 X^3 X^2 X^2 X^3 X^2  0 X^3  0
 0  0  0 X^3+X^2 X^2 X^3 X^2 X^2  0  0 X^2 X^3+X^2 X^3 X^3  0 X^2 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+22x^14+56x^15+97x^16+204x^17+276x^18+206x^19+88x^20+36x^21+22x^22+8x^23+6x^24+2x^27

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.