The generator matrix

 1  0  0  1  1  1 X^2 X^2  1  1 X^2  1  1 X^2  0  1  1 X^2+X  1  1  1  X X^2+X  1  1 X^2+X  1
 0  1  0  0  1 X+1  1  0 X^2 X+1  1  0  1  1  1  X X+1  1 X^2+X X^2+1  0  1  1 X+1 X^2+X+1  1 X^2+1
 0  0  1  1  1  0 X+1  1  0 X^2 X+1 X+1 X^2+X+1  X  0 X^2+1 X^2+X X^2+X X^2 X^2+1 X+1 X^2+X X^2+X+1 X^2 X+1 X^2 X+1
 0  0  0  X  0  X  X  0  0  X  X X^2+X X^2 X^2 X^2+X X^2 X^2 X^2+X  X  X X^2  X  0 X^2  X  X X^2
 0  0  0  0  X  X X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2  0  X X^2  X X^2 X^2+X X^2  X  X X^2 X^2+X  X  X  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+62x^21+221x^22+492x^23+650x^24+932x^25+1200x^26+1144x^27+1173x^28+936x^29+605x^30+446x^31+219x^32+68x^33+22x^34+12x^35+5x^36+2x^37+2x^39

The gray image is a linear code over GF(2) with n=108, k=13 and d=42.
This code was found by Heurico 1.16 in 1.02 seconds.