The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  1  1  1  1  1 X^2  1
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^2+X X^3+X^2 X^2 X^3+X^2+X X^2+X  0 X^3  X X^3+X^2 X^2+X  0 X^2 X^3+X^2+X X^3  X  0
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3+X^2+X  X X^3  0 X^2+X X^3+X X^3+X^2 X^3 X^3+X^2+X X^2 X^2 X^2+X X^3+X^2  0 X^3+X^2+X X^2+X X^2  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+45x^24+166x^25+151x^26+320x^27+142x^28+148x^29+38x^30+4x^32+6x^33+2x^34+1x^50

The gray image is a linear code over GF(2) with n=216, k=10 and d=96.
This code was found by Heurico 1.16 in 0.016 seconds.