The generator matrix

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

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+141x^20+336x^21+1028x^22+1406x^23+2826x^24+3060x^25+5147x^26+4612x^27+5386x^28+3308x^29+2801x^30+1312x^31+881x^32+268x^33+205x^34+28x^35+13x^36+4x^37+3x^38+2x^39

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 11.8 seconds.