The generator matrix

 1  0  0  1  1  1 X^2+X  1 X^3+X^2+X  1  1 X^2  1 X^3+X  X  X  1  1
 0  1  0  1 X^3+X X^2+X+1  1 X^2+X X^2 X^2+X+1 X^3  1 X+1  1  1  1 X^3+X^2+1  0
 0  0  1  1 X^2+1  X X+1 X+1  1 X^2  X X^2+X+1 X^2+1  0 X^3+X^2  X X^3+X^2+X+1  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  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+62x^14+368x^15+984x^16+1436x^17+2556x^18+1424x^19+902x^20+336x^21+94x^22+16x^23+9x^24+4x^25

The gray image is a linear code over GF(2) with n=144, k=13 and d=56.
This code was found by Heurico 1.16 in 0.25 seconds.