The generator matrix

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

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+120x^13+273x^14+620x^15+981x^16+1238x^17+1594x^18+1472x^19+997x^20+508x^21+213x^22+132x^23+36x^24+6x^25+1x^28

The gray image is a linear code over GF(2) with n=72, k=13 and d=26.
This code was found by Heurico 1.16 in 7.16 seconds.