The generator matrix

 1  0  0  0  1  1  1 X^2+X  1  X X^2  1  0 X^2  0  1  1  1
 0  1  0  0  0  1  1  1 X^2 X^2+X  1 X+1 X^2+X  1  1  1  1  0
 0  0  1  0  1  1  0 X+1 X^2+X+1  1 X^2+1 X+1  X  X X^2+X+1  0  1  0
 0  0  0  1  1  0 X+1  1  X X^2+X+1  0 X^2  1 X^2+1 X+1 X^2+X  0  0
 0  0  0  0  X X^2  X  X X^2+X  0  X  X  X  0 X^2 X^2+X  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+104x^12+238x^13+619x^14+1200x^15+1929x^16+2630x^17+2830x^18+2736x^19+2048x^20+1146x^21+564x^22+224x^23+78x^24+18x^25+18x^26+1x^30

The gray image is a linear code over GF(2) with n=72, k=14 and d=24.
This code was found by Heurico 1.13 in 0.563 seconds.