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 X^2 X^2  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X^3+X  0 X^2+X X^3 X^3+X^2+X X^3 X^3+X^2+X X^2 X^3+X X^3+X^2  0  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0
 0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0

generates a code of length 27 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+13x^24+60x^25+81x^26+212x^27+82x^28+36x^29+14x^30+12x^31+1x^50

The gray image is a linear code over GF(2) with n=216, k=9 and d=96.
This code was found by Heurico 1.16 in 6.87e-008 seconds.