The generator matrix

 1  0  0  0  1  1  1 X^2  1 X^2+X  1 X^2+X  0  1  0  1  1  1  1  1  1  1 X^2  1  X  1  1
 0  1  0  0  0  1  1  1 X^2+X  1 X^2+X  1  0 X^2+X+1  1 X+1 X^2+1  X X^2+X+1  0 X^2+1 X^2  X  0 X^2+X X^2+X  1
 0  0  1  0  1  1  0  1 X^2  0  1 X^2+X+1  1 X^2+X X^2+X+1 X+1 X^2+1 X^2+1 X^2+X X^2+X X^2+1  0  0 X^2+X+1  1  X  1
 0  0  0  1  1  0  1 X+1 X^2+X+1 X+1  X  X X+1 X^2  1  1 X^2+X X+1  1 X^2+X+1 X^2+1 X^2  1 X^2+1 X^2+X+1 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  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+123x^20+446x^21+736x^22+1862x^23+2094x^24+4082x^25+4215x^26+5630x^27+4196x^28+4166x^29+2150x^30+1810x^31+681x^32+390x^33+128x^34+42x^35+9x^36+4x^37+2x^38+1x^42

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 11.4 seconds.