The generator matrix

 1  0  0  0  0  1  1  1  1 X^2  1  1  X  1  1 X^2+X X^2  1  0  0 X^2 X^2+X  1  1  1  1 X^2
 0  1  0  0  0  0 X^2  0  0 X^2 X^2+X+1 X^2+1  1 X+1 X+1  1 X^2+X  X  1  1  1 X^2+X  1 X^2+1 X^2 X+1  1
 0  0  1  0  0  0  1 X^2 X+1  1 X^2+X+1  1 X^2+X  1 X^2 X^2+X+1  0  X  X X+1 X^2+X  1 X^2+X+1  0 X+1  X  0
 0  0  0  1  0  1  1  X  0 X^2+1  0 X^2+X X^2+X X^2+X+1 X^2+X X+1  1  1 X^2+X+1 X^2  1 X^2 X+1 X^2+X+1  0 X+1  X
 0  0  0  0  1  1  X X+1 X+1 X+1 X^2+1 X^2  1 X^2+X+1 X^2+1 X^2 X^2+1 X^2+X X^2+1  0 X^2 X^2+X+1  0  1 X^2+X  X X+1
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  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+238x^20+894x^21+1757x^22+3198x^23+4942x^24+7250x^25+9180x^26+9902x^27+9778x^28+7694x^29+5138x^30+3018x^31+1457x^32+662x^33+244x^34+138x^35+32x^36+12x^37+1x^38

The gray image is a linear code over GF(2) with n=108, k=16 and d=40.
This code was found by Heurico 1.13 in 15.5 seconds.