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  X
 0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2
 0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0
 0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  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+21x^24+32x^26+128x^27+67x^28+6x^32+1x^52

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 0.0071 seconds.