The generator matrix

 1  0  1  1  1 X^2  1  1 X^2  1  1 X^2 X^2+X  1  1  1  1 X^2
 0  1  1  0  1  1 X+1 X^2  1 X^2+X X^2+1  1  1 X^2  1 X+1  0  1
 0  0  X  0  0  0  0  X  X X^2+X X^2+X  X X^2  X X^2  0  X  X
 0  0  0  X  0  X  X  X X^2+X X^2 X^2+X X^2+X  X  0  X  0  X X^2
 0  0  0  0  X X^2  X X^2+X X^2+X  X X^2  X X^2+X X^2 X^2 X^2  0 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+60x^13+146x^14+256x^15+475x^16+710x^17+820x^18+714x^19+460x^20+248x^21+122x^22+52x^23+24x^24+6x^25+2x^27

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 0.137 seconds.