The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  1  X  0 X^2  1  1 X^2
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^2+X  X X^2+X  X X^3+X  X X^3 X^3 X^3+X^2  0
 0  0 X^3+X^2  0 X^2  0  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3+X^2 X^3
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2  0 X^2 X^2 X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  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+119x^14+200x^15+562x^16+704x^17+968x^18+688x^19+530x^20+192x^21+95x^22+8x^23+27x^24+2x^26

The gray image is a linear code over GF(2) with n=144, k=12 and d=56.
This code was found by Heurico 1.16 in 0.079 seconds.