The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+90x^11+498x^12+1746x^13+4065x^14+8794x^15+15587x^16+22222x^17+25100x^18+21906x^19+15918x^20+9022x^21+3830x^22+1654x^23+508x^24+98x^25+28x^26+4x^27+1x^30

The gray image is a linear code over GF(2) with n=72, k=17 and d=22.
This code was found by Heurico 1.13 in 24.1 seconds.