The generator matrix

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

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+72x^20+360x^21+1118x^22+1356x^23+2954x^24+3154x^25+4896x^26+4488x^27+5418x^28+3398x^29+2888x^30+1228x^31+933x^32+318x^33+120x^34+32x^35+30x^36+2x^37+2x^38

The gray image is a linear code over GF(2) with n=108, k=15 and d=40.
This code was found by Heurico 1.13 in 4.13 seconds.