The generator matrix

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

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+54x^21+279x^22+424x^23+667x^24+936x^25+1102x^26+1254x^27+1139x^28+1002x^29+632x^30+356x^31+232x^32+52x^33+34x^34+14x^35+9x^36+4x^37+1x^38

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 1.09 seconds.