The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+17x^24+8x^25+14x^26+176x^27+14x^28+8x^29+17x^30+1x^54

The gray image is a linear code over GF(2) with n=108, k=8 and d=48.
This code was found by Heurico 1.16 in 0.00816 seconds.