The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  1 X^3+X^2  0 X^3  1  1  1
 0  X  0  X  0 X^3 X^2+X X^2 X^2+X  0 X^3+X^2+X X^3+X^2  X  X X^2 X^3+X X^3 X^2+X
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^3+X^2 X^3 X^2+X X^2  0 X^2+X  0  X X^3+X X^3+X^2+X  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 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+83x^14+150x^15+554x^16+568x^17+1420x^18+540x^19+550x^20+136x^21+63x^22+14x^23+15x^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 0.062 seconds.