The generator matrix
1 1 1 1 1 1 1 1 1 X 1 X 0 0 X^2 X X 1
0 X 0 0 0 0 0 0 0 X X X^2 X X^2 X X^2+X X^2 0
0 0 X 0 0 0 X X^2+X X X X 0 X X 0 X^2 0 0
0 0 0 X 0 X X X^2+X 0 0 0 X X^2 X^2+X X^2 X^2+X X 0
0 0 0 0 X X 0 X^2+X X 0 X^2 X^2 X X X^2+X X^2+X 0 0
0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0
0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0
0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0
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+68x^10+64x^11+242x^12+326x^13+702x^14+1082x^15+1787x^16+2606x^17+2578x^18+2642x^19+1814x^20+1106x^21+694x^22+302x^23+244x^24+58x^25+50x^26+6x^27+8x^28+4x^30
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 1.5 seconds.