The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1 X^2  1  X  X  1
 0 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3  0 X^3+X^2 X^3  0 X^3+X^2 X^3
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3  0 X^2 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 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+14x^14+58x^15+43x^16+266x^17+276x^18+260x^19+30x^20+52x^21+14x^22+2x^23+4x^24+2x^25+2x^28

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 3.62e-008 seconds.