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^3+X^2  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3 X^3 X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^3  0 X^3+X^2 X^3 X^3  0
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3 X^3 X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^2 X^2  0  0  0
 0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  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+9x^24+24x^25+22x^26+400x^27+22x^28+24x^29+9x^30+1x^54

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 0.016 seconds.