The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X^2 0 1 X X^2 X^2 0
0 X 0 0 0 0 0 X^2 X^2 X X^2+X X^2+X X^2+X X^2+X X^2 0 X^2+X X 0 X^2 X X X 0 X^2 X 0
0 0 X 0 0 X^2 X^2+X X X X X X^2+X 0 X X^2 X 0 X X^2+X X 0 X^2+X X^2+X X X 0 X^2
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X X^2+X X 0 X^2+X X^2+X 0 X^2+X X^2+X 0 X^2 X^2 X X^2+X X^2 X^2+X X
0 0 0 0 X X X^2 X^2+X X X^2+X X^2 0 X X^2+X X^2+X X X X X^2+X X^2 X^2+X X X^2+X X^2+X X^2+X X 0
generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+150x^22+60x^23+274x^24+116x^25+370x^26+152x^27+382x^28+136x^29+170x^30+44x^31+133x^32+4x^33+46x^34+10x^36
The gray image is a linear code over GF(2) with n=108, k=11 and d=44.
This code was found by Heurico 1.16 in 1.75 seconds.