The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+126x^16+4x^17+152x^18+200x^20+180x^21+748x^22+384x^23+1796x^24+840x^25+3096x^26+1280x^27+3120x^28+840x^29+1836x^30+384x^31+761x^32+180x^33+200x^34+136x^36+4x^37+100x^38+4x^40+8x^42+4x^46

The gray image is a linear code over GF(2) with n=108, k=14 and d=32.
This code was found by Heurico 1.16 in 3.71 seconds.