The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X^2 X 1 1 X^2 1 X X^2 1 1 1 X^2
0 X 0 X 0 0 X X^2+X 0 X^2 X X^2+X 0 X^2+X X X X X^2 0 X X^2+X X^2 X 0 X^2 0 0
0 0 X X 0 X^2+X X 0 X^2 X X 0 X^2 X^2+X X X X^2+X X X^2+X X^2+X 0 X X 0 0 X^2+X X^2
0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2
0 0 0 0 X^2 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0
0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2
0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0
generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 21.
Homogenous weight enumerator: w(x)=1x^0+48x^21+85x^22+116x^23+135x^24+210x^25+338x^26+288x^27+208x^28+206x^29+192x^30+100x^31+37x^32+46x^33+22x^34+8x^35+2x^37+3x^38+3x^40
The gray image is a linear code over GF(2) with n=108, k=11 and d=42.
This code was found by Heurico 1.16 in 46.2 seconds.