The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+38x^10+8x^11+133x^12+136x^13+648x^14+1096x^15+1657x^16+2824x^17+3236x^18+2904x^19+1666x^20+1112x^21+648x^22+88x^23+118x^24+24x^25+38x^26+9x^28

The gray image is a linear code over GF(2) with n=72, k=14 and d=20.
This code was found by Heurico 1.16 in 0.836 seconds.