The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+46x^18+108x^19+269x^20+522x^21+428x^22+1170x^23+548x^24+2586x^25+708x^26+3380x^27+768x^28+2794x^29+675x^30+1204x^31+396x^32+406x^33+169x^34+88x^35+62x^36+28x^37+21x^38+2x^39+3x^40+1x^42+1x^44

The gray image is a linear code over GF(2) with n=108, k=14 and d=36.
This code was found by Heurico 1.16 in 5.18 seconds.