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.