The generator matrix

 1  0  0  1  1  1  X  1  1  1  1 X^2 X^2  1  X  1  1 X^2  1  1  1 X^2  1  1  0  0  1
 0  1  0  1 X^2+X X^2+X+1  1 X^2  0 X+1 X+1  1  1 X^2+1  X X^2  X  X X^2+1 X+1  1  X  X X^2+X X^2+X  1  0
 0  0  1  1 X^2+X+1 X^2+X  1  X X+1 X+1  0  X  1 X+1  1  1 X^2+X  1  0  0  1  1 X^2+X  0  1 X^2  0
 0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0
 0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  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 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 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+23x^20+124x^21+288x^22+326x^23+747x^24+772x^25+1226x^26+1118x^27+1281x^28+804x^29+766x^30+338x^31+235x^32+92x^33+22x^34+10x^35+15x^36+2x^38+1x^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 0.792 seconds.