The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+50x^13+166x^14+224x^15+568x^16+622x^17+839x^18+624x^19+573x^20+222x^21+145x^22+48x^23+7x^24+2x^25+1x^26+3x^28+1x^30

The gray image is a linear code over GF(2) with n=72, k=12 and d=26.
This code was found by Heurico 1.16 in 0.109 seconds.