The generator matrix

 1  0  1  1  1  0  1  1  X  1 X^2+X  1  1  1  0 X^2  1  1 X^2+X  1  0  1  1  1  X X^2 X^2
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+1  1 X^2 X^2+X X+1  1  1  0 X^2+X+1  1 X^2+1  1 X^2 X+1 X^2+1  1  X  1
 0  0  X X^2+X  0 X^2+X  X X^2+X  X  0 X^2  X  0 X^2  0  X  0  X X^2  0 X^2 X^2+X  0  0 X^2+X  X  X
 0  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  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+54x^20+78x^21+274x^22+238x^23+797x^24+734x^25+1428x^26+1006x^27+1453x^28+666x^29+808x^30+282x^31+241x^32+58x^33+44x^34+10x^35+12x^36+6x^38+1x^40+1x^44

The gray image is a linear code over GF(2) with n=108, k=13 and d=40.
This code was found by Heurico 1.16 in 1.06 seconds.