The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  X  X  1  0  1  0  1  X  0  X  1  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2  0 X^2+X  X X^2+X X^2+X X^2+X X^2+X  X  0  X  0 X^2+X  X X^2+X  0 X^2
 0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  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+123x^20+152x^22+64x^23+556x^24+256x^25+680x^26+384x^27+798x^28+256x^29+424x^30+64x^31+272x^32+24x^34+39x^36+2x^40+1x^48

The gray image is a linear code over GF(2) with n=108, k=12 and d=40.
This code was found by Heurico 1.16 in 16.4 seconds.