The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+106x^15+181x^16+142x^17+189x^18+184x^19+104x^20+64x^21+26x^22+14x^23+10x^24+2x^25+1x^26

The gray image is a linear code over GF(2) with n=72, k=10 and d=30.
This code was found by Heurico 1.16 in 0.0187 seconds.