The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+227x^20+220x^21+1096x^22+1280x^23+2722x^24+3364x^25+5074x^26+4616x^27+5322x^28+3364x^29+2758x^30+1264x^31+980x^32+220x^33+222x^34+8x^35+27x^36+2x^38+1x^48

The gray image is a linear code over GF(2) with n=108, k=15 and d=40.
This code was found by Heurico 1.16 in 13.2 seconds.