The generator matrix
1 0 0 0 1 1 1 X^2 X^2+X 1 X^2+X 1 X 1 1 X^2+X 1 1
0 1 0 0 0 1 1 1 1 X 0 X+1 1 X^2 X^2+1 X^2 X+1 1
0 0 1 0 1 1 0 1 1 X+1 1 X 0 0 X+1 X^2 1 1
0 0 0 1 1 0 1 X+1 X X X+1 X 1 1 X+1 1 X^2+1 X^2
0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0
0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2
0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0
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+245x^12+176x^13+1432x^14+1512x^15+4830x^16+4456x^17+7384x^18+4464x^19+5026x^20+1504x^21+1288x^22+168x^23+264x^24+8x^25+8x^26+1x^28+1x^32
The gray image is a linear code over GF(2) with n=72, k=15 and d=24.
This code was found by Heurico 1.16 in 4.89 seconds.