The generator matrix
1 0 0 0 0 1 1 1 1 X^2+X X X^2 1 1 1 1 X 1
0 1 0 0 0 0 X^2 1 X^2+1 1 X 1 X X+1 1 X^2+X X^2 X+1
0 0 1 0 0 0 1 X^2 X^2+X+1 X^2+1 1 1 X X^2+1 X^2+X+1 1 X^2+X X^2+1
0 0 0 1 0 1 1 X^2+X+1 X 1 1 1 X^2 X^2+X+1 X+1 0 1 X^2+X
0 0 0 0 1 1 X X X^2 0 1 X^2+1 X^2+X+1 X^2+1 X^2+X X^2 X^2+X+1 X+1
0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2
generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+274x^12+824x^13+2208x^14+4372x^15+7791x^16+11108x^17+12192x^18+11272x^19+7898x^20+4480x^21+2096x^22+676x^23+288x^24+36x^25+16x^26+4x^28
The gray image is a linear code over GF(2) with n=72, k=16 and d=24.
This code was found by Heurico 1.13 in 7.09 seconds.