The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+130x^19+645x^20+1534x^21+3238x^22+6114x^23+10012x^24+14946x^25+18763x^26+19906x^27+18889x^28+15342x^29+10315x^30+6002x^31+3086x^32+1318x^33+513x^34+228x^35+70x^36+12x^37+3x^38+4x^39+1x^40

The gray image is a linear code over GF(2) with n=108, k=17 and d=38.
This code was found by Heurico 1.13 in 56.8 seconds.