The generator matrix

 1  0  0  0  1  1  1  X  1  1  1  1  1 X^3  1  1 X^2+X  1
 0  1  0  0 X^2 X^3+1 X^2+1  1 X^2+X X^3+X+1 X^2+1 X^3+X X^3+X^2+X+1  0 X^3+X+1 X^3+X^2 X^3+X  X
 0  0  1  0 X^2+1  1 X^2 X^2+X+1 X^3+X^2+1 X^2+X X^3+X^2+X+1 X^3+X^2  1 X^2+X X^3+X^2+X X^3+X^2  1  0
 0  0  0  1  1 X^2 X^2+X+1 X^2+1 X^2+X  X X+1 X^3+X^2+X+1 X^3  1 X^3+1 X^3+X^2+1 X^3+X^2+X+1 X^3+1
 0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 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 13.

Homogenous weight enumerator: w(x)=1x^0+186x^13+1145x^14+4928x^15+12991x^16+28186x^17+35699x^18+28992x^19+13068x^20+4510x^21+1071x^22+256x^23+20x^24+14x^25+5x^26

The gray image is a linear code over GF(2) with n=144, k=17 and d=52.
This code was found by Heurico 1.16 in 24.4 seconds.