The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+49x^10+66x^11+193x^12+252x^13+735x^14+1028x^15+1865x^16+2748x^17+2522x^18+2744x^19+1834x^20+1044x^21+750x^22+252x^23+198x^24+52x^25+37x^26+6x^27+5x^28+3x^30

The gray image is a linear code over GF(2) with n=72, k=14 and d=20.
This code was found by Heurico 1.16 in 1.35 seconds.