The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1 X^2  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^2 X^3  0 X^3+X^2 X^2  0  0 X^2  0 X^3 X^3
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0
 0  0  0 X^3  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  0
 0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 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+106x^24+128x^26+512x^27+248x^28+12x^32+16x^36+1x^48

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 64.7 seconds.