The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  1  1  X  X  1  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2 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  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0  0  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+158x^16+52x^20+32x^22+460x^24+320x^26+2048x^27+420x^28+160x^30+297x^32+92x^36+44x^40+12x^44

The gray image is a linear code over GF(2) with n=108, k=12 and d=32.
This code was found by Heurico 1.16 in 0.295 seconds.