The generator matrix

 1  0  0  0  1  1  1  X  1  1  1 X^2+X  0 X^2+X X^2+X  1 X^2  1
 0  1  0  0 X^2  1 X^2+1  1 X^2+X  X X+1  0  1  1  X X^2+1  X X^2+X
 0  0  1  0 X^2+1  1 X^2 X^2+X+1  1  0 X^2+X+1  1  X X^2+X  1 X+1  1 X^2+X
 0  0  0  1  1 X^2 X^2+X+1 X^2+X+1  X  1 X+1 X^2+X+1 X^2+X+1 X^2+1 X^2+X+1 X^2+1  1 X^2

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+174x^14+370x^15+560x^16+522x^17+809x^18+574x^19+614x^20+292x^21+136x^22+30x^23+9x^24+2x^25+1x^26+2x^27

The gray image is a linear code over GF(2) with n=72, k=12 and d=28.
This code was found by Heurico 1.16 in 0.115 seconds.