The generator matrix

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

generates a code of length 18 over Z2[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+90x^11+230x^12+298x^13+593x^14+1136x^15+1653x^16+2560x^17+3180x^18+2580x^19+1768x^20+1156x^21+566x^22+288x^23+178x^24+80x^25+12x^26+2x^27+10x^28+2x^29+1x^30

The gray image is a linear code over GF(2) with n=72, k=14 and d=22.
This code was found by Heurico 1.16 in 4.14 seconds.