The generator matrix

 1  0  0  0  1  1  1 X^2+X  1  1 X^3+X  1 X^3+X^2+X  1 X^3 X^3+X^2  1  X
 0  1  0  0  X X^2 X^3+X X^2+X X^2+1 X^3+X^2+X+1  1 X^3+X^2+X+1  1  1 X^3+X^2  1  X  1
 0  0  1  0 X^3 X^2+1 X^3+X^2+1  1 X^2+X+1  1  X X^2+X X^3+1 X^3+X^2+X+1 X^2+X X^2+X+1 X^3+X X^2
 0  0  0  1 X^3+1  1 X^3 X^3+X^2+1  X X^3+X+1 X^3+1 X^3+X^2+1 X^3+X^2+X X^2  1  1 X^3+X^2+X+1  1

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+644x^14+2426x^15+7004x^16+13388x^17+18320x^18+13860x^19+7102x^20+2100x^21+580x^22+94x^23+13x^24+4x^27

The gray image is a linear code over GF(2) with n=144, k=16 and d=56.
This code was found by Heurico 1.16 in 9.28 seconds.