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.