The generator matrix

 1  0  1  1  1  0  1 X^2+X  1 X^2  1  1  1  X  1  X  1  0
 0  1  1  0 X^2+X+1  1 X^2+X  1 X+1  1  0 X^2+X+1 X^2  1 X^2+1 X^2 X^2  1
 0  0  X  0 X^2+X  X X^2 X^2+X  X  0  X X^2  0  X  0  X X^2  0
 0  0  0  X  0  X X^2 X^2+X  X  X X^2+X  X  X X^2  0  0  0 X^2
 0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 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+54x^13+186x^14+288x^15+434x^16+678x^17+814x^18+688x^19+440x^20+290x^21+150x^22+48x^23+20x^24+2x^25+2x^26+1x^32

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 9.28 seconds.