The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0  X  1  0  X  X  X  1  1  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  0  0  0  X  X  X X^2  X X^2+X  X X^2 X^2+X X^2+X X^2
 0  0  X  0  X  X X^2+X  0  0  0  X  X X^2+X X^2  X  X X^2 X^2 X^2  0  X  X  0 X^2+X  X X^2+X  0
 0  0  0  X  X  0 X^2+X  X X^2  X X^2  0 X^2+X X^2+X  X X^2+X X^2  X  0  X X^2  X  X  0  X  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  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 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+208x^20+426x^22+112x^23+889x^24+528x^25+1430x^26+800x^27+1747x^28+480x^29+858x^30+112x^31+427x^32+16x^33+98x^34+52x^36+4x^38+3x^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 1.53 seconds.