The generator matrix

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

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+355x^24+640x^26+780x^28+224x^30+41x^32+4x^36+3x^40

The gray image is a linear code over GF(2) with n=216, k=11 and d=96.
This code was found by Heurico 1.16 in 12.8 seconds.