The generator matrix

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

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+108x^13+292x^14+610x^15+938x^16+1422x^17+1412x^18+1516x^19+903x^20+608x^21+260x^22+82x^23+29x^24+6x^25+4x^26+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 1.11 in 0.156 seconds.