The generator matrix

 1  0  0  0  0  1  1  1 X^2  1  0  X  1 X^2+X  1  1 X^2+X  1
 0  1  0  0  0 X^2  1 X^2+1  1 X^2  X X^2+X X+1  1  X  1  1  0
 0  0  1  0  0 X^2+X+1 X+1  X X^2+X+1  X  1  1  1 X^2+1 X^2+1 X^2 X+1  0
 0  0  0  1  0  1  X X^2+1 X^2+X+1 X+1  X X^2+X+1 X^2+X+1 X^2  0 X+1  0  0
 0  0  0  0  1  1 X^2  X  X X^2+X+1 X^2+1 X^2+X+1 X^2 X^2  X X^2+1  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+103x^12+458x^13+1157x^14+2130x^15+3824x^16+5524x^17+6161x^18+5716x^19+4005x^20+2178x^21+959x^22+346x^23+163x^24+32x^25+11x^26

The gray image is a linear code over GF(2) with n=72, k=15 and d=24.
This code was found by Heurico 1.13 in 2.06 seconds.