The generator matrix

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

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+176x^20+492x^22+638x^24+384x^25+1736x^26+1280x^27+1804x^28+384x^29+688x^30+424x^32+152x^34+28x^36+4x^38+1x^48

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 1.56 seconds.